Simple Harmonic Motion
- Simple harmonic motion (SHM) is a specific type of oscillation
- An oscillation is said to be SHM when:
The acceleration of a body is proportional to its displacement but acts in the opposite direction
- Acceleration a and displacement x can be represented by the defining equation of SHM:
a ∝ −x
- The two conditions required for an object to be simple harmonic motion are therefore:
- The acceleration is proportional to the displacement
- The acceleration is in the opposite direction to the displacement
Force, acceleration and displacement of a pendulum in SHM
Worked example
Explain why a person jumping on a trampoline is not an example of simple harmonic motion.
Step 1: Recall the conditions for simple harmonic motion
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- The conditions required for SHM:
- The restoring force/acceleration is proportional to the displacement
- The restoring force/acceleration is in the opposite direction to the displacement
- The conditions required for SHM:
Step 2: Consider the forces in the scenario given
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- When the person is not in contact with the trampoline, the restoring force is equal to their weight, which is constant
- The value of their weight does not change, even if they jump higher (increase displacement)
Step 3: Write a concluding sentence
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- The restoring force on the person is not proportional to their distance from the equilibrium position, therefore, this scenario does not fulfil the conditions for SHM
