AP Physics - Waves and SHM
Simple Harmonic Motion
Spring Oscillations
The force exerted by the spring depends on the displacement
Hook’s Law
F = -K X
The minus sign on the force indicates that it is a restoring force
Directed to restore the mass to its equilibrium position
K is the spring constant
The force is not constant, so the acceleration is not constant either
Force Varies = Acceleration Varies
Displacement is measured from the equilibrium point
Amplitude
Maximum displacement
Cycle
A full to-and-fro motion
Period
The time required to complete one cycle
Frequency
The number of cycles completed per cycle
Any vibrating system where the restoring force is proportional to the negative of the displacement is in SHM
Called a simple harmonic oscillator
Energy in SHM
Ue = ½ K X2
If the mass is at the limits of its motions, the energy is all potential
If the mass is at the equilibrium point, the energy is all kinetic
Potential energy is at the turning points
The Simple Pendulum
A simple pendulum consists of a mass at the end of a lightweight cord
Assume that the cord does not stretch, and that its mass is negligible
Period depends on the length
In order to be in SHM, the restoring force must be proportional to the negative of the displacement