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

Answer:

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

$d = \dfrac{1}{5}\sin 2t$.....(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.

$a = \dfrac{1}{5}$

So, the maximum displacement is

$d= \dfrac{1}{5}\ inch$

We need to calculate the frequency

$\omega=2\pi f$

$f = \dfrac{1}{\pi}\ Hz$

We need to calculate the time required for one cycle

$t =\dfrac{1}{f}$

$t =\pi\ sec$

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