Simple Harmonic Motion

Question 1

Displacement, Amplitude, Period, Frequency, Angular frequency, phase difference

Answer 1

Displacement the distance an object has moved from its mean/rest position.

Amplitude the maximum displacement.

Period the time for one complete pattern of oscillation.

Frequency the number of oscillations per unit of time (Hz = per second).

Angular frequency (ω) 2πf radians per unit of time.

Phase difference (ф) the angle, in radians, between two oscillations.

Question 2

Simple Harmonic Motion

Answer 2

Restoring Force (& acceleration) is proportional to the displacement from the equilibrium position (centre) and in the direction opposite to the displacement (directed towards the equilibrium).

         a = -cx 

c = (2πf)2, squared as the constant must be positive to preserve the sign (direction)
Hence the definition becomes
a = -(2πf)2x (note: ω = 2πf)

two solutions to this equation are:
x = A sin (2πft) and x = A cos (2πft) — use dependant on initial condition

velocity = -A ω sin (ωt), with max velocity when sin() = 1