Simple Harmonic Motion

Simple Harmonic Motion (SHM) periodic motion about an equilibrium point where the restoring force is proportional to the distance from equilibrium Periodic motion: Repeated motion Equilibrium position: Position where object will come to rest. Fnet = 0 For oscillation to be SHM, the forces must always be directed to the center of symmetrical oscillation and the force must be proportional to the displacement.

Simple Harmonic Motion (SHM) Examples: Pendulum Spring Liquid in U-tube

SHM and Waves Simple Harmonic Motion- Pendulum Waves Visualization_SHM_Pendulum Visualization_SHM_BlockSpring Visualization_SHM_LiquidInUTube

Simple Harmonic Motion (SHM) Displacement vs. Time Graph Sinusoid Wave Properties period (T) amplitude displacement (m) time (s) frequency (f) = #cycles per second midline = equilibrium position

Amplitude maximum displacement from equilibrium Relates to the amount of energy Unit: meters

Simple Harmonic Motion pendulum (small angles) mass on spring amplitude = A amplitude = A equilibrium equilibrium amplitude = -A amplitude = -A equilibrium equilibrium amplitude = A amplitude = A

Velocity / Force / Acceleration At equilibrium Velocity is at a maximum Net force is zero Acceleration is zero At maximum amplitude Velocity is zero Net force is at a maximum Acceleration is at its maximum

What happens as the pendulum moves? At point D: equilibrium At point A: At point G: Restoring force works to slow down bob, so it will return to equilibrium.

What happens as the pendulum moves?

Period & Frequency Period (T): time it takes to complete one cycle Unit: seconds Frequency (f): number of cycles or vibrations per unit of time Unit: 1/sec = Hertz (Hz)

Example 1 An angry bird flaps its wings every 1.2 seconds. What is the period and frequency of the wings’ motion?

Example 1 An angry bird flaps its wings every 1.2 seconds. What is the period and frequency of the wings’ motion?