For a simple harmonic motion (SHM) to occur, the following elements need be present:
- The SHM is always stationary at the maximums and minimums. For example, a when a pendulum is swinging at it's highest, it will always be stationary at that moment.
- The displacement after an infinite amount of time will end up at zero where the equilibrium and displacement=0 is at the middle point.
- The equilibrium will have maximum velocity.
- There is negative and positive displacement from the equilibrium position.
- Velocity is always zero when displacement is at a maximum.
- Kinetic energy --> Potential energy --> Kinetic energy.
- The SHM will always have a fixed time period.
Graphs Of SHM
F -xWhere x = displacement and F = restoring force. Due to force causing acceleration...
a -xWhere a = acceleration. After long calculations, we can some to the solution as:
x = Acos(2πf)tWhere A = amplitude, f = frequency and t = time.
- Proportional to the distance from equilibrium position.
- Pointing towards the equilibrium position.
- The displacement of a SHM is x = Acos(2πf)t.
- The gradient of displacement against time graph produces the velocity against time graph. This is because V = dx/dt (change in displacement / change in time).
- The gradient of velocity against time graph produces the acceleration against time graph. This is because a = dv/dt (change in velocity / change in time).