Find a model for simple harmonic motion that has an initial displacement (t=0) of 0 inches, an amplitude of 5 inches, and a frequency 4/3 cycles per second.

The equation of simple harmonic motion is

Explanation:

Given that,

Amplitude = 5 inches

Frequency

As per the question initial displacement is zero at t = 0 for sine curve.

The displacement is zero so the phase difference will be zero.

We know that,

The general equation of simple harmonic motion

Where, A = amplitude

= angular frequency

= phase shift

We need to calculate the time period

Using formula of frequency

Put the value into the formula

We need to calculate the angular frequency

Using formula of angular frequency

Put the value into the general equation

Hence, The equation of simple harmonic motion is

true tan speed = ang vel x radius