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