Conditions for Simple Harmonic Motion
- Simple harmonic motion (SHM) is a specific type of oscillation
- SHM is defined as:
A type of oscillation in which the acceleration of a body is proportional to its displacement, but acts in the opposite direction
- Examples of oscillators that undergo SHM are:
- The pendulum of a clock
- A mass on a spring
- Guitar strings
- The electrons in alternating current flowing through a wire
- This means for an object to oscillate specifically in SHM, it must satisfy the following conditions:
- Periodic oscillations
- Acceleration proportional to its displacement
- Acceleration in the opposite direction to its displacement
- Acceleration a and displacement x can be represented by the defining equation of SHM:
a ∝ −x
- An object in SHM will also have a restoring force to return it to its equilibrium position
- This restoring force will be directly proportional, but in the opposite direction, to the displacement of the object from the equilibrium position
- Note: the restoring force and acceleration act in the same direction
Force, acceleration and displacement of a pendulum in SHM
- This is why a person jumping on a trampoline is not an example of simple harmonic motion:
- The restoring force on the person is not proportional to their distance from the equilibrium position
- When the person is not in contact with the trampoline, the restoring force is equal to their weight, which is constant
- This does not change, even if they jump higher
