# Harmonic Motion and Resonance- Physics B G494

- Created by: Laura
- Created on: 03-05-13 22:36

**Harmonic Motion**

*A body executes SHM when its acceleration is directly proportional to its displacement but in the opposite direction. *

**Simple harmonic motion is an idealised time of oscillating motion.**

**Quantity** **Symbol** **Definition** **Units:**

- Amplitude (A): the maximum displacement from the equilibrium position. Units = m
- Period (T): the time for one complete oscillation. Units = s
- Frequency (f): the number of oscillations in 1 second. Note that f = 1/T Hz
- Displacement (s): how far the object is from its equilibrium (rest) position. Units= m

The vertical displacement of a mass on a spring varies sinusoidally with time:

**s = Asinwt (A=Amplitude, w= 2 x pi x f)**

The velocity of a mass on a spring also varies this way,however when displacement is greatest, the velocity is zero, therefore the velocity forms a cosine graph.

**v = wAcoswt When velocity is max, v=wA**

Acceleration is the change in velocity over time (dv/dt), so to get the acceleration we must differentiate the equation for velocity to get:

**a = -w^2Asinwt** (therefore a=-w^2s)

- the resultant force will be proportional to the displacement ( as …

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