Question

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.

Answer 1

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

Step-by-step explanation:

Given that,

The equation of simple harmonic motion

`d = (1)/(5)\sin 2t`.....(I)

We need to calculate the maximum amplitude

Using equation of simple harmonic motion

`y = a \sin\omega t`

Where, a = amplitude

`\omega` =frequency

t = time

On comparing equation (I) and general equation

The amplitude is a maximum displacement traveled by a wave.

`a = (1)/(5)`

So, the maximum displacement is

`d= (1)/(5)\ inch`

We need to calculate the frequency

`\omega=2\pi f`

`f = (1)/(\pi)\ Hz`

We need to calculate the time required for one cycle

`t =(1)/(f)`

`t =\pi\ sec`

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