(SHM) Regents Physics

Harmonic Motion is cyclic and/or repetitive Cycle- has a beginning and an end - all motion repeats Oscillator- object that displays a cyclic nature - Examples: 1. pendulum 2. moon revolving around Earth 3. vibration of a guitar string

Describing a cycle Period (T):time for 1 cycle units: seconds(s) Frequency (f):number of cycles per second units: Hertz (Hz) 1 Hz = 1 cycle= 1 cycle second s Frequency and Period are inverses of each other: T = 1 f = _ 1_ f T

Describing a cycle Amplitude (A):how “big” the cycle is - directly related to energy - units vary: ˚, m, volts, etc. - largest change from equilibrium 30˚ Equilibrium Amplitude

Visual Representation of SHM Time (s) Position (cm) A = f = T = # of cycles = A = 10 cm f = ½ Hz T = 2 s # of cycles = 3

Describing a Cycle Phase - “where” an oscillator is in its cycle - described using a sine/cosine function 0˚ 360˚ 270˚ 180˚ 90˚ 0˚ 90˚ Time Position 180˚ 270˚ 360˚

In Phase When 2 or more oscillators are at the same phase in their cycle at the same time

Out of Phase When 2 or more oscillators are at different phases in their cycle at the same time 90˚ out of phase

Natural Frequency Frequency at which an oscillator tends to vibrate when disturbed - Directly related to magnitude of restoring force (how much force pulls the oscillator back to equilibrium) - Greater restoring force = higher natural frequency - Inversely related to the inertia of the system - Greater inertia= lower natural frequency

Resonance When a force is applied at the natural frequency. A maximum increase in amplitude will occur Example: When you push another person on a swing, when should you push so that they go higher? When they are highest in their swing and push in the same direction

Damping - Reduction in amplitude because of friction - Energy is removed from the system *An upper limit exists on the energy that can be added to a system because as amplitude increases, the natural frequency also increases Example: car shocks