Simple Harmonic Motion

Simple Harmonic Motion

1. If an object changes shape when a force is applied and can return to its original shape once the force is removed, it is elastic

2. When an object has a force pushing down on it, the force acting in the opposite direction trying to return it to its original position is the restoring force

3. Hooke's Law

   • Hooke's Law states that when an object is bent, stretched or compressed by a displacement(s), the restoring force (F) is directly proportional to the displacement if the elastic limit is not reached
   • F = -ks
     • F = restoring force
     • -k = elastic constant
     • s = displacement
   • Examples of systems that obey Hooke's Law
     • A mass vibrating up and down at the end of a string
     • Each prong on a vibrating tuning fork
     • A small angle of swing in a pendulum
     • The tides in the ocean
     • A magnet suspended horizontally from a piece of thread

4. Simple Harmonic Motion

   • A body is said to be moving with simple harmonic motion if its acceleration is directly proportional to its distance from a fixed point on its path and its acceleration is always directed towards that point
   • a = -ω²s
     • a = acceleration
     • ω² = constant
     • s = displacement
   • Definitions
     • A cycle or oscillation is the movement from point A to point B and then back to point A
     • The periodic time or the period (T) is the time taken to complete one oscillation
     • The frequency (f) is the number of cycles occurring per second
     • The amplitude is the greatest displacement that the particle has from the equilibrium position
     • One cycle per second is called one hertz (Hz)
   • The oscillations per second of Simple Harmonic Motion is 1/f or 1/T
   • The period of Simple Harmonic Motion is T = 2π/ω

5. Pendulum

   • The length of the pendulum is the distance from a fixed point of suspension to the centre of gravity of the bob
   • Period of a pendulum
   • Experiment to demonstrate the relationship between the period and the length of a simple pendulum and hence, calculate gravity - pg. 152

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