Simple Harmonic Motion

AQA A - Simple Harmonic Motion

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  • Created on: 03-01-13 12:55
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Simple Harmonic motion
A body will oscillate with simple harmonic motion if the resorting force acting on it (pulling the body
back towards a rest position) is directly proportional to the body's displacement. A restoring force
results in an acceleration which is in the opposite direction to the body's displacement.
The conditions for simple harmonic motion are summarized by:
a x
Where a is acceleration and x is displacement. The minus sign shows that the acceleration is in the
opposite direction to the displacement vector.
Simple harmonic motion and circular motion
An object on a turntable rotating with constant speed will have a constant angular velocity, . When
viewed from the side the object moves in a straight line with simple harmonic motion where:
= 2/T = 2f
T is the time for one oscillation and f is the frequency or number of oscillations per second.
Phase and phase difference
Different points on the rim of a spinning wheel are said to be out of step out of phase. The phase
difference between any 2 points is the angle between them. When the term phase is applied to
waves and oscillations more generally, one complete oscillation is taken to be equivalent to one
rotation or 2 radians and phase differences are measured in radians.

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Graphs and Equations for simple harmonic motion
The equations and graphs work for continuous, undamped simple harmonic motion.
Damping complicates things by reducing the amplitude over time.
The oscillator must already br oscillating before time t=0
Displacement against time
The displacement x of a particle vibrating with shm is given by:
x = A sin t
Velocity against time
Velocity is the rate of increase in displacement.…read more


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