An object moves in simple harmonic motion described by the equation d equals one fifth sine 2 t where t is measured in seconds and d in inches. find the maximum displacement, the frequency, and the time required for one cycle.

The maximum displacement, the frequency, and the time required for one cycle are 1/5 inch, 1/π Hz and π sec.

Explanation:

Given that,

The equation of simple harmonic motion

.....(I)

We need to calculate the maximum amplitude

Using equation of simple harmonic motion

Where, a = amplitude

=frequency

t = time

On comparing equation (I) and general equation

The amplitude is a maximum displacement traveled by a wave.

So, the maximum displacement is

We need to calculate the frequency

We need to calculate the time required for one cycle

Hence, The maximum displacement, the frequency, and the time required for one cycle are 1/5 inch, 1/π\ Hz and π\ sec.