Answer to Question #100334 in Differential Equations for May

Question

How can harmonic motion be described mathematically? Be sure to link correct mathematical terms to correct physics terms – for example, how are the amplitude, period length, and other mathematical properties of harmonic motion waves related to how an object is moving?

Answer 1

Harmonic motion is a special type of periodic or oscillatory motion, in which restoring force is directly proportional to displacement and act in opposite direction

F=-kx

The terms associated with harmonic motions are as follows..

Frequency which is inversely proportional to time period.

Thus, f=1/T;

F=-kx;

also F=ma.

Thus, ma=-kx.

Thus, a=(-k/m)x.

Complete solution is

x(t)=Acos(2πft),

where x is the displacement which is the function of time t, A is the amplitude, f is the frequency.