Optics, waves and sound

what is displacement (x)?

The distance of the mass from the equilibrium point at any moment (with a + or – sign)

what is amplitude (A)?

The maximum displacement—the greatest distance from the equilibrium point.

what is a cycle

The complete to-and-fro motion from some initial point back to that same point (e.g., from x=−A to x=+A and back to x=−A).

What is the period (T)?

The time required to complete one cycle.

What is frequency (f)?

The number of complete cycles per second. It is generally specified in hertz (Hz), where 1 Hz = 1 cycle per second (s⁻¹)

displacement, amplitude, cycle, period, frequency

100/1.25HZ = 80s

Both (b) and (d) will give simple harmonic motion because they give the force as minus a constant times a displacement. The displacement need not be x, but the minus sign is required to restore the system to equilibrium, which is why (c) does not produce SHM.

What is the defining characteristic of simple harmonic motion (SHM)?

Any oscillating system for which the net restoring force is directly proportional to the negative of the displacement (F=−kx

What is another name for an object or system exhibiting simple harmonic motion?

A simple harmonic oscillator (SHO).

What three conditions must a force equation meet to produce simple harmonic motion?

1. The force must be proportional to the displacement (e.g., F∝y).

2. It must be multiplied by a constant (e.g.F=−2.3y).

3. It must have a minus sign (negative), indicating the force is a restoring force directed toward equilibrium.
   (Note: The variable representing displacement does not have to be x; it can be y, θ, etc.)

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