# Simple Harmonic Motion

• Simple harmonic motion (SHM) is a special type of oscillation
• SHM occurs when a system has a stable equilibrium, and a restoring force which is linearly proportional to the distance from that equilibrium
• Amplitude controls the maximum displacement from equilibrium
• Angular frequency controls the rate of oscillation
• Phase angle specifies the conditions at time = 0
• The square of angular frequency is equal to the force constant of an oscillator, divided by its mass
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We can write this requirement for SHM in another way. Remember Newton's Second Law:

If we replace the F in Hooke's Law with ma, we get

or, if we write the derivative all by itself,

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Q:  The vocal cords of an opera singer
vibrate back and forth with a period
of 0.8 milliseconds.

What is the frequency of their oscillation?

What is the angular frequency of their oscillation?

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