Simple harmonic motion questions and answers pdf unlocks the secrets of oscillatory motion. Dive into a world of springs, pendulums, and waves, exploring the fundamental principles that govern these fascinating phenomena. This comprehensive guide provides a wealth of knowledge, from basic definitions to complex problem-solving strategies. Prepare to master simple harmonic motion, from the foundational concepts to the real-world applications.
This resource delves into the intricacies of simple harmonic motion (SHM), offering a thorough explanation of its core concepts. It details the key characteristics, mathematical representations, real-world examples, applications, problem-solving strategies, and visual representations of SHM. We also explore related concepts like resonance, damping, and forced oscillations, along with how SHM manifests in different physical systems. This comprehensive guide equips you with the tools and knowledge to tackle SHM problems with confidence.
Introduction to Simple Harmonic Motion
Simple Harmonic Motion (SHM) is a fundamental concept in physics that describes a special type of oscillatory motion. Imagine a weight swinging back and forth on a spring, or a pendulum bobing rhythmically. These are classic examples of SHM. It’s a recurring pattern that shows up in many surprising places, from the vibrations of atoms to the oscillations of stars.SHM is characterized by a restoring force that always acts to bring the system back to its equilibrium position.
This is crucial, as it dictates the rhythmic nature of the motion. The force is directly proportional to the displacement from equilibrium, and it’s always directed towards the equilibrium point. This predictable relationship leads to a consistent and beautiful pattern of movement.
Key Characteristics of Simple Harmonic Motion
Understanding the key characteristics is essential to grasping the essence of SHM. The restoring force, a crucial factor, is directly proportional to the displacement from the equilibrium position. This is mathematically expressed as F = -kx, where F is the restoring force, k is the spring constant, and x is the displacement. The negative sign indicates that the force always acts in the opposite direction of the displacement.The period of SHM is the time taken for one complete oscillation.
It depends on the system’s properties, such as the mass and the spring constant. A heavier mass will take longer to oscillate, while a stiffer spring will result in a faster oscillation. The amplitude, on the other hand, is the maximum displacement from the equilibrium position. It dictates the extent of the oscillation.
Relationship Between SHM and Oscillatory Motion, Simple harmonic motion questions and answers pdf
Oscillatory motion, in general, involves a repetitive back-and-forth movement around a central point. Simple Harmonic Motion is aspecific* type of oscillatory motion where the restoring force is directly proportional to the displacement. This crucial proportionality is what distinguishes SHM from other forms of oscillatory motion.
Comparison of SHM with Other Oscillatory Motions
| Characteristic | Simple Harmonic Motion (SHM) | Damped Oscillation | Forced Oscillation |
|---|---|---|---|
| Restoring Force | Proportional to displacement, always directed towards equilibrium | Proportional to displacement, but magnitude decreases over time | External force drives the oscillation |
| Amplitude | Constant, if no external forces are applied | Decreases over time | Can be constant or change depending on the driving force |
| Period | Constant, depending on the system’s properties | Increases over time | Can be constant or change depending on the driving frequency |
| Energy | Conserved, assuming no energy loss | Decreases over time due to energy dissipation | Can be constant or change depending on the driving force and system characteristics |
The table above provides a concise comparison of SHM with other oscillatory motions, highlighting the key differences in terms of restoring force, amplitude, period, and energy.
Mathematical Representation of SHM
Simple Harmonic Motion (SHM) is a fundamental concept in physics, describing the oscillatory motion of many systems. Understanding its mathematical representation unlocks the secrets behind springs, pendulums, and even atoms vibrating. It’s the mathematical language of rhythmic movement, providing a framework for analyzing and predicting these regular patterns.The core of SHM lies in its mathematical equations, which precisely describe the motion’s characteristics.
These equations, derived from Newton’s laws of motion, form the basis for predicting displacement, velocity, and acceleration at any given time during the oscillation. This allows us to quantify the rhythm of these systems.
Displacement Equation
The displacement of an object undergoing SHM is a sinusoidal function of time. It describes the object’s position relative to its equilibrium point. This sinusoidal nature is crucial; it’s the hallmark of oscillatory motion. Understanding displacement is fundamental to grasping the entire picture of SHM.
x(t) = A cos(ωt + φ)
Where:
- x(t) represents the displacement at time t.
- A is the amplitude, the maximum displacement from the equilibrium position.
- ω is the angular frequency, related to the frequency (f) by ω = 2πf, determining the oscillation’s speed.
- t is the time.
- φ is the phase constant, which indicates the starting position or phase of the oscillation.
Velocity Equation
The velocity of the object undergoing SHM is also sinusoidal, but it’s 90 degrees out of phase with the displacement. This phase difference is crucial to understanding the motion’s dynamics.
v(t) = -Aω sin(ωt + φ)
Where:
- v(t) represents the velocity at time t.
Acceleration Equation
The acceleration of the object is directly proportional to its displacement, but in the opposite direction. This is a key characteristic of SHM, a direct link between position and acceleration.
a(t) = -ω2x(t)
Where:
- a(t) represents the acceleration at time t.
Summary of Equations
| Equation | Variable | Description |
|---|---|---|
| x(t) = A cos(ωt + φ) | x(t), A, ω, t, φ | Displacement as a function of time |
| v(t) = -Aω sin(ωt + φ) | v(t) | Velocity as a function of time |
| a(t) = -ω2x(t) | a(t) | Acceleration as a function of time |
Example Scenarios
A simple pendulum swinging or a mass attached to a spring oscillating are classic examples of SHM. The equations allow us to precisely predict the pendulum’s position, speed, and acceleration at any point in its swing. Imagine calculating the position of a swinging grandfather clock pendulum at any given moment. That’s the power of these equations.
Examples of Simple Harmonic Motion
Simple harmonic motion (SHM) isn’t just a theoretical concept; it’s a fundamental principle that governs countless phenomena in our everyday world. From the swinging of a pendulum to the vibrations of a guitar string, SHM provides a framework for understanding these motions. Let’s delve into some captivating examples and explore the underlying principles.Understanding the restoring force is key to recognizing SHM.
A restoring force is a force that always acts to return an object to its equilibrium position. This is the heart of SHM; the object’s acceleration is directly proportional to its displacement from equilibrium, and always directed back towards that point. The period and frequency of SHM are also critical aspects to consider; they describe the time it takes for one complete oscillation and the number of oscillations per unit time, respectively.
Pendulum Motion
A simple pendulum, consisting of a mass suspended from a fixed point, exhibits SHM when its displacement from the vertical is small. The restoring force is provided by gravity, pulling the mass back towards the equilibrium position. The period of a simple pendulum depends on the length of the string and the acceleration due to gravity. A longer pendulum will have a longer period, and stronger gravity will decrease the period.
Mass-Spring System
A mass attached to a spring is another classic example of SHM. When the mass is displaced from its equilibrium position, the spring exerts a restoring force proportional to the displacement, pulling the mass back towards the equilibrium position. The period of oscillation depends on the mass of the object and the spring constant. A stiffer spring (higher spring constant) results in a shorter period.
Vibrating String
A vibrating string, like those on a musical instrument, also exhibits SHM. When plucked or struck, the string vibrates back and forth, with the restoring force arising from the tension in the string. The period and frequency of the vibrations depend on the tension in the string, the mass per unit length, and the length of the string itself.
Other Examples
Many other systems display SHM, including:
- A child on a swing (small displacements): The restoring force is provided by gravity and the tension in the swing ropes. The period depends on the length of the swing ropes.
- A vibrating tuning fork: The restoring force arises from the elasticity of the metal in the fork. The period is determined by the material properties and the geometry of the fork.
- The oscillations of a simple circuit: The restoring force arises from the interplay of electrical and magnetic fields. The period is influenced by the capacitance and inductance of the circuit.
Quantitative Analysis of SHM Examples
The following table summarizes the characteristics of some common SHM examples.
| Example | Restoring Force | Period (T) | Frequency (f) | Amplitude |
|---|---|---|---|---|
| Simple Pendulum | Gravity | 2π√(L/g) | 1/2π√(g/L) | Maximum displacement from equilibrium |
| Mass-Spring System | Spring force (Hooke’s Law) | 2π√(m/k) | 1/2π√(k/m) | Maximum displacement from equilibrium |
| Vibrating String | String tension | Depends on string properties | Depends on string properties | Maximum displacement from equilibrium |
Note: Values for period and frequency are dependent on the specific parameters of each system.
Applications of Simple Harmonic Motion
Simple harmonic motion (SHM) isn’t just a theoretical concept; it’s a fundamental principle that underpins countless technologies and natural phenomena. From the swing of a pendulum to the vibrations of a guitar string, SHM provides a framework for understanding and predicting the behavior of oscillating systems. Its widespread applicability stems from its elegant mathematical description, which allows us to model and analyze a diverse range of motions.SHM’s beauty lies in its ability to simplify complex oscillatory movements.
This simplicity allows engineers and scientists to design and predict the behavior of systems ranging from simple clocks to sophisticated communication devices. Understanding the underlying principles of SHM is crucial for anyone working in fields like engineering, physics, and even music. The predictable nature of SHM allows for the precise control and design of various devices.
Applications in Mechanical Systems
SHM plays a crucial role in a multitude of mechanical systems. Understanding the principles of SHM is vital for designing machines that operate efficiently and reliably. The predictable nature of SHM allows engineers to anticipate and mitigate potential problems related to vibrations. Accurate design relies on understanding the oscillatory behavior of components.
- Clocks: The pendulum in a grandfather clock is a classic example of SHM. The precise period of oscillation allows for accurate timekeeping. The regularity of the pendulum’s swing is a direct consequence of its SHM. This predictable behavior is essential for the functionality of timekeeping devices.
- Springs: Springs exhibit SHM when subjected to a restoring force. This property is utilized in various mechanical systems, such as shock absorbers in vehicles and spring-loaded toys. The ability of springs to oscillate in a predictable manner is a direct consequence of the underlying principles of SHM.
- Vibrating Machines: Many industrial machines utilize vibrations based on SHM principles. These machines often require precise control of vibrations to maintain functionality and prevent damage. Predicting the behavior of vibrations is crucial for maintaining optimal performance and safety.
Applications in Electrical and Electronic Systems
SHM’s influence extends to electrical and electronic systems, where oscillations are essential for communication and signal processing. The predictable nature of oscillations in these systems enables reliable data transmission and manipulation.
- Alternating Current (AC) Circuits: The sinusoidal nature of AC voltage and current is directly related to SHM. This fundamental relationship is exploited in various electronic devices and power systems. Understanding SHM allows for efficient design and operation of electrical systems.
- Radio Waves: Radio waves, used for communication, are generated and received through oscillating electric and magnetic fields. The principles of SHM are crucial in understanding and controlling these oscillations, enabling the efficient transmission and reception of information.
- Musical Instruments: The vibrations of strings, air columns, and other components in musical instruments follow SHM patterns. This knowledge helps musicians and instrument makers to achieve desired sounds and tones. The ability to control and predict the oscillations of these instruments is essential for producing specific musical notes and harmonies.
Applications in Physics and Other Fields
Beyond mechanical and electrical applications, SHM principles underpin many physical phenomena. The predictable nature of SHM provides a powerful tool for understanding and modeling these phenomena.
- Astronomy: The orbits of planets and celestial bodies, while not strictly SHM, often exhibit periodic behavior that can be approximated by SHM. This approximation is useful in understanding and predicting the movements of celestial objects.
- Molecular Vibrations: Atoms within molecules vibrate, and these vibrations are often described by SHM. Understanding these vibrations is essential for analyzing molecular structures and properties.
- Biology: Certain biological systems exhibit periodic behavior, such as the rhythmic beating of the heart. SHM principles can be applied to model and analyze these biological oscillations.
A Summary of Applications
| Field | Application | Underlying Principle |
|---|---|---|
| Mechanical | Pendulums, springs, vibrating machines | Restoring force and periodic oscillation |
| Electrical/Electronic | AC circuits, radio waves | Sinusoidal oscillations and wave propagation |
| Physics/Other | Celestial bodies, molecular vibrations, biological rhythms | Periodic motion and restoring forces |
Problem-Solving Strategies for SHM
Unlocking the secrets of Simple Harmonic Motion (SHM) often involves a blend of analytical thinking and strategic application of fundamental principles. Mastering problem-solving techniques is crucial for confidently tackling SHM scenarios, from basic oscillations to more complex scenarios. This section will guide you through the process of approaching SHM problems with clarity and precision.Effective problem-solving hinges on a systematic approach.
We’ll delve into the key steps, provide illustrative examples, and explore different strategies to help you develop a robust understanding of SHM. It’s not just about getting the right answer; it’s about grasping the underlying physics and applying it creatively.
Understanding the Problem Statement
A crucial first step involves a meticulous analysis of the problem statement. Identify the given quantities, including initial conditions, and the unknowns that need to be determined. This meticulous examination lays the groundwork for selecting the appropriate equations and variables. Clearly defining the system and its constraints is vital.
Selecting Relevant Equations
Identifying the applicable equations is a critical juncture in SHM problem-solving. Familiarize yourself with the fundamental equations describing SHM, including those related to displacement, velocity, acceleration, period, frequency, and energy. Choosing the correct equation hinges on a thorough understanding of the specific situation and the relationships between the variables.
Identifying Variables and Constants
Accurately identifying the variables and constants within the problem is crucial. This involves recognizing the quantities that are given, the ones that are to be determined, and the constants inherent in the system, such as the spring constant or the mass of the object. Careful attention to units is paramount.
Solving for the Unknown
This stage involves substituting the known variables into the relevant equations and performing the necessary calculations. Pay close attention to units and ensure they are consistent throughout the process. A systematic approach will ensure accuracy and prevent errors. For example, if you’re calculating velocity, make sure your units are consistent (meters per second).
Example 1: Spring-Mass System
A spring with a spring constant of 20 N/m is attached to a mass of 0.5 kg. The mass is displaced 0.1 meters from its equilibrium position and released. Determine the period of oscillation.
Period (T) = 2π√(m/k)
Substituting the given values, we have:T = 2π√(0.5 kg / 20 N/m) ≈ 0.99 s
Example 2: Pendulum
A simple pendulum with a length of 1 meter is released from a small angle. Determine the period of oscillation.
Period (T) = 2π√(L/g)
where L is the length of the pendulum and g is the acceleration due to gravity (approximately 9.81 m/s²).Substituting the values, we get:T = 2π√(1 m / 9.81 m/s²) ≈ 2.01 s
Example 3: Damped Oscillation
A damped oscillator has an equation of motion given by x(t) = Ae^(-bt)cos(ωt). Determine the time it takes for the amplitude to reduce to half its initial value.This example illustrates the use of more complex equations in SHM problems, demonstrating that a solid understanding of the equations is crucial for problem-solving. The solution involves algebraic manipulation and the understanding of exponential decay and trigonometric functions.
Analyzing SHM Questions and Answers
Simple Harmonic Motion (SHM) problems often appear in various physics courses, testing your understanding of oscillatory motion. Mastering these problems involves more than just plugging numbers into formulas; it’s about applying fundamental principles and interpreting the results within the context of the physical system. This section will delve into common SHM issues and provide strategies for tackling them effectively.Understanding SHM goes beyond rote memorization.
It’s about grasping the underlying concepts of restoring forces, displacement, velocity, acceleration, and how they relate to each other. Developing a strong intuition for these relationships is key to successfully navigating complex SHM problems.
Common SHM Problem Types
Recognizing the various types of SHM problems encountered in education is crucial for effective problem-solving. These problems typically involve scenarios like springs, pendulums, and waves, often requiring the application of different equations and problem-solving techniques. Identifying the key characteristics of each scenario is the first step to tackling these problems successfully.
- Determining the period and frequency of oscillation given the spring constant and mass.
- Calculating the displacement, velocity, and acceleration of an object at a specific time.
- Analyzing the motion of a simple pendulum under different conditions.
- Finding the equilibrium position and amplitude of a system exhibiting SHM.
- Determining the total energy of a simple harmonic oscillator.
Problem-Solving Approaches
Effective problem-solving involves more than just applying formulas. Strategies such as drawing diagrams, identifying the given variables, and determining the relevant equations are vital to successfully navigating these problems.
- Visualizing the System: Creating a clear diagram of the physical system is often the first and most important step. Visualizing the forces acting on the object and the object’s position in relation to its equilibrium point is crucial. This step helps to clearly define the problem’s parameters.
- Identifying Known and Unknown Variables: Carefully identify the variables provided in the problem statement. This step ensures that you focus on the specific information needed to solve the problem.
- Selecting the Appropriate Equations: Choosing the correct equations based on the physical situation is crucial. This often involves recognizing the type of SHM involved (spring, pendulum, etc.).
- Solving for the Unknown Variables: Apply the selected equations to determine the unknown variables, carefully substituting the known values. Carefully consider the units of each variable to ensure consistency.
- Interpreting the Results: The final step involves evaluating the obtained solution within the context of the problem. Does the solution make physical sense? Are the units correct? This step ensures accuracy and a deeper understanding of the problem.
Sample SHM Problems
These examples demonstrate the application of the strategies Artikeld.
| Problem Statement | Solution |
|---|---|
| A spring with a spring constant of 20 N/m is stretched 0.2 m from its equilibrium position. What is the potential energy stored in the spring? |
|
| A simple pendulum with a length of 1 m swings with a period of 2 seconds. What is the acceleration due to gravity at the location of the pendulum? |
|
Interpreting Results
Interpreting the results from SHM problems is crucial to understanding the physical meaning of the solutions. Understanding the context of the problem, such as the units of the variables, is vital to understanding the outcome.
- Unit Consistency: Ensure that all units are consistent throughout the calculations. Inconsistent units will lead to incorrect results.
- Physical Meaning: Evaluate the solution in terms of the physical situation described in the problem. Does the answer make sense in the context of the problem? For example, a negative velocity could indicate motion in the opposite direction from the initial direction.
- Limitations of the Model: Recognize that the SHM model is an approximation. Real-world systems may deviate from the ideal SHM model due to factors like air resistance or friction.
Visual Representation of Simple Harmonic Motion: Simple Harmonic Motion Questions And Answers Pdf
Simple harmonic motion (SHM) is a fundamental concept in physics, describing the oscillatory motion of many systems. Visualizing this motion through graphs provides a powerful tool to understand and predict its behavior. These graphical representations reveal key characteristics of the motion, such as the relationship between displacement, velocity, and acceleration over time. Graphs of SHM allow us to easily identify the patterns and make predictions about the future behavior of the system.Understanding the visual representations of SHM allows for a deeper insight into the underlying mechanisms driving the oscillatory motion.
This understanding is crucial in various applications, from analyzing the behavior of a pendulum to understanding the vibrations of a musical instrument.
Displacement-Time Graph
The displacement-time graph of SHM is a sinusoidal curve. The shape of this curve directly reflects the oscillatory nature of the motion. The amplitude of the curve represents the maximum displacement from the equilibrium position, while the period represents the time taken for one complete oscillation. The graph clearly shows the pattern of the object’s position changing over time, repeating itself periodically.
For example, a pendulum’s displacement-time graph would show the bob’s position oscillating back and forth symmetrically around its equilibrium position.
Velocity-Time Graph
The velocity-time graph of SHM is also a sinusoidal curve, but it is shifted in phase with respect to the displacement-time graph. The maximum velocity occurs at the equilibrium position (zero displacement), and the velocity is zero at the maximum displacement points. The graph’s amplitude is proportional to the maximum velocity of the oscillation. For instance, the velocity-time graph of a mass attached to a spring would show a sinusoidal wave with its peak value at the zero displacement point and zero values at the maximum displacement points.
Acceleration-Time Graph
The acceleration-time graph of SHM is also a sinusoidal curve, but it is shifted in phase with respect to both the displacement-time and velocity-time graphs. The acceleration is maximum at the maximum displacement points and is zero at the equilibrium position. The amplitude of the curve is proportional to the maximum acceleration of the oscillation. This graph displays the changing force acting on the object throughout the cycle, with its direction constantly changing.
The graph of a mass on a spring, for example, would show a sinusoidal wave with its peak values at the maximum displacement points and a zero value at the equilibrium position.
Visual Summary of SHM Graphs
| Graph Type | Shape | Amplitude | Period | Phase Relationship | Key Feature |
|---|---|---|---|---|---|
| Displacement-Time | Sinusoidal | Maximum displacement | Time for one oscillation | In phase with itself | Shows position over time |
| Velocity-Time | Sinusoidal | Maximum velocity | Time for one oscillation | 90° out of phase with displacement | Shows velocity over time |
| Acceleration-Time | Sinusoidal | Maximum acceleration | Time for one oscillation | 180° out of phase with displacement | Shows acceleration over time |
Concepts Related to Simple Harmonic Motion
Simple harmonic motion (SHM) is a fundamental concept in physics, describing the oscillatory motion of a system around an equilibrium position. Beyond the basic sinusoidal nature of SHM, several crucial concepts influence and modify its behavior. These concepts, like resonance, damping, and forced oscillations, are vital to understanding real-world systems exhibiting oscillatory characteristics.
Resonance
Resonance is a phenomenon where a system oscillates with maximum amplitude at a specific frequency, known as the resonant frequency. This occurs when the driving force’s frequency matches the system’s natural frequency. Imagine pushing a child on a swing; if you push at the right rhythm, the swing will swing higher and higher. This synchronized rhythm is resonance.
- Resonance occurs when the driving frequency matches the natural frequency of the system.
- The amplitude of oscillation increases significantly at resonance.
- Examples of resonance include musical instruments (tuning), bridges (wind-induced oscillations), and electronic circuits (tuning radios).
Damping
Damping is the reduction in amplitude of oscillations over time due to resistive forces like friction or air resistance. Think of a pendulum swinging; eventually, it slows down and stops due to air resistance and friction at the pivot point. This gradual decrease in oscillation amplitude is damping.
- Damping is caused by resistive forces acting on the oscillating system.
- Over time, damping reduces the amplitude of oscillation, eventually bringing the system to rest.
- Examples of damping include a vibrating tuning fork that eventually stops, or a car’s suspension system absorbing shocks.
Forced Oscillations
Forced oscillations occur when an external periodic force acts on a system that would naturally oscillate. This force can cause the system to oscillate at the frequency of the driving force. A child on a swing pushed by another person is a simple example.
- Forced oscillations occur when an external periodic force acts on a system.
- The system oscillates at the frequency of the driving force.
- Examples include a child’s swing pushed by another person, a building vibrating from an earthquake, or a mechanical system driven by an external motor.
Comparison of Concepts
| Concept | Description | Effect on Motion | Example |
|---|---|---|---|
| Resonance | Maximum amplitude at specific frequency | Increased amplitude | Tuning a radio to a specific station |
| Damping | Reduction in amplitude over time | Decreased amplitude, eventual stop | Pendulum slowing down |
| Forced Oscillations | External periodic force drives oscillation | Oscillation at driving frequency | Pushing a swing |
SHM in Different Systems
Simple harmonic motion (SHM) isn’t confined to a single system; it’s a fundamental concept that governs a surprisingly wide range of phenomena. From the gentle sway of a pendulum to the rapid oscillations of a sound wave, SHM provides a powerful framework for understanding these diverse motions. Let’s delve into how SHM manifests in various physical systems.The underlying principle in all SHM systems is the restoring force.
This force acts to pull the system back towards its equilibrium position, creating a cyclical motion. The strength of this restoring force is directly proportional to the displacement from equilibrium, a key characteristic of SHM. This consistent relationship is what allows us to model and predict the behavior of these systems.
Springs
Understanding SHM in springs is crucial, as it forms the basis for many mechanical systems. A spring’s inherent elasticity generates a restoring force directly proportional to the extension or compression from its equilibrium length. This straightforward relationship directly relates to Hooke’s Law, which defines the restoring force as F = -kx, where k is the spring constant and x is the displacement from equilibrium.
The resulting motion is a sinusoidal oscillation, characterized by a period dependent on the mass attached and the spring constant.
Pendulums
Pendulums, whether simple or physical, provide another compelling example of SHM. A simple pendulum, consisting of a mass suspended from a string, exhibits SHM for small angles of oscillation. The restoring force is provided by gravity, acting tangentially to the circular path of the bob. The period of oscillation, in this case, is primarily dependent on the length of the pendulum and the acceleration due to gravity.
For larger angles, the motion deviates from simple harmonic motion, becoming approximately sinusoidal. This subtle difference is important for understanding the limitations of the SHM model.
Waves
Waves, encompassing sound, light, and water waves, also exhibit SHM. Consider a transverse wave, like a wave on a string. Each particle in the medium oscillates about its equilibrium position in a sinusoidal pattern, with the displacement being perpendicular to the direction of wave propagation. The restoring force arises from the tension in the string, or the medium’s elasticity in other wave forms.
The wave’s properties, such as frequency and amplitude, directly relate to the SHM characteristics of the constituent particles.
Summary Table
| System | Restoring Force | Period Dependence | Characteristics |
|---|---|---|---|
| Spring | Hooke’s Law: F = -kx | Mass (m) and Spring Constant (k) | Sinusoidal oscillation, directly proportional to displacement |
| Simple Pendulum | Gravity | Length (l) and Acceleration due to gravity (g) | Approximately sinusoidal for small angles, period depends on length and gravity |
| Waves (e.g., transverse wave) | Tension/Medium Elasticity | Medium properties, frequency | Sinusoidal oscillation of particles, perpendicular to wave direction |
