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Simple Harmonic Motion

Simple Harmonic Motion. (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

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Simple Harmonic Motion

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  1. Simple Harmonic Motion (SHM) Regents Physics

  2. 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

  3. 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

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

  5. Visual Representation of SHM 10 0 Position (cm) Time (s) 1 4 5 6 2 3 10 A = A = 10 cm T = T = 2 s # of cycles = # of cycles = 3 f = f = ½ Hz

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

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

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

  9. 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

  10. 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

  11. 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

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