What is the Difference Between Simple Harmonic Motion and Periodic Motion?
🆚 Go to Comparative Table 🆚The main difference between simple harmonic motion and periodic motion lies in the nature of the motion and the forces involved. Here are the key differences:
Simple Harmonic Motion:
- In simple harmonic motion, the displacement of the object is always in the opposite direction of the restoring force.
- The acceleration of the object is directly proportional to the displacement and acts in the opposite direction, which means the motion can be described by a second-order linear differential equation.
- The period of oscillation does not depend on the amplitude of the motion, and the motion can be described using trigonometric functions.
Periodic Motion:
- In periodic motion, the displacement of the object may or may not be in the direction of the restoring force.
- The motion is oscillatory and repeats itself, but the acceleration of the object is not necessarily directly proportional to the displacement and acting in the opposite direction.
- The period of oscillation can vary depending on the amplitude of the motion, and the motion can be described using various mathematical functions.
In summary, simple harmonic motion is a specific type of periodic motion where the acceleration of the object is directly proportional to the displacement and acts in the opposite direction. In contrast, periodic motion is a more general term that refers to any oscillatory motion, including simple harmonic motion.
On this pageWhat is the Difference Between Simple Harmonic Motion and Periodic Motion? Comparative Table: Simple Harmonic Motion vs Periodic Motion
Comparative Table: Simple Harmonic Motion vs Periodic Motion
Here is a table comparing the differences between simple harmonic motion and periodic motion:
Feature | Simple Harmonic Motion (SHM) | Periodic Motion |
---|---|---|
Definition | An oscillatory motion where the restoring force is directly proportional to the displacement of the body from its mean position, and the acceleration is given by Hooke's Law. | A motion that repeats itself after an equal interval of time, with no equilibrium position and no specific restoring force. |
Equilibrium | A stable equilibrium position exists. For example, the equilibrium position of a mass on a spring is the place where the mass is returned to its original position. | There is no stable equilibrium position. Uniform circular motion is an example of periodic motion without an equilibrium position. |
Displacement | Displacement in simple harmonic motion as a function of time is given by $$x(t)=X\cos\left(\frac{2\pi t}{T}\right),$$ where X is the amplitude of the motion. | The displacement of the system does not vary with simple harmonic functions (sine or cosine). |
Velocity | The velocity function for simple harmonic motion is given by $$v(t)=-v{\text{max}}\text{sin}\left(\frac{2\pi t}{T}\right),$$ where $$v{\text{max}} = \sqrt{\frac{k}{m}}X$$. | The velocity function does not follow a simple harmonic function and may vary with other functions, like sine or cosine. |
Acceleration | The acceleration function for simple harmonic motion is given by $$a(t)=-\frac{kX}{m}\cos\left(\frac{2\pi t}{T}\right)$$. | The acceleration function does not follow a simple harmonic function and may vary with other functions, like sine or cosine. |
Read more:
- Oscillatory Motion vs Periodic Motion
- Oscillation vs Simple Harmonic Motion
- Frequency vs Period
- Circular Motion vs Rotational Motion
- Circular Motion vs Spinning Motion
- Simple Pendulum vs Compound Pendulum
- Perpetual vs Periodic
- Periodic vs Progressive Waves
- Linear Motion vs Non Linear motion
- Oscillation vs Vibration
- Cycle vs Period
- Kinematics vs Dynamics
- Newton’s First Law vs Second Law of Motion
- Kinetics vs Kinematics
- Uniform Motion vs Non Uniform Motion
- Damped vs Undamped Vibration
- Lagrangian vs Hamiltonian Mechanics
- Damped Oscillation vs Forced Oscillation
- Fundamental Frequency vs Natural Frequency