Chapter 8, Problem 40RE

(a)

To determine

To describe: The motion of the object.

Answer to Problem 40RE

The motion of the object is simple harmonic motion.

Explanation of Solution

Given: $d=6\sin \left(2t\right)$

The equation of simple harmonic motion is given by,

  $y=a\cos \omega t$

And the given equation is,

  $d=6\sin \left(2t\right)$

Therefore, the motion of the object is simple harmonic motion.

(b)

To determine

To find: The maximum displacement.

Answer to Problem 40RE

The maximum displacement is $6$ .

Explanation of Solution

Given: $d=6\sin \left(2t\right)$

The equation of simple harmonic motion is given by,

  $y=a\cos \omega t$

And the given equation is,

  $d=6\sin \left(2t\right)$

The amplitude is $6$ .

Therefore, the maximum displacement is $6$ .

(c)

To determine

To find: The time required for one oscillation.

Answer to Problem 40RE

The time required for one oscillation is $\pi$ .

Explanation of Solution

Given: $d=6\sin \left(2t\right)$

The equation of simple harmonic motion is given by,

  $y=a\cos \omega t$

And the given equation is,

  $d=6\sin \left(2t\right)$

  $\begin{array}{c}T=\frac{2\pi }{\omega }\\ =\frac{2\pi }{2}\\ =\pi \end{array}$

The time required for one oscillation is $\pi$ .

(d)

To determine

To find: The time required for one oscillation.

Answer to Problem 40RE

The frequency is $\frac{1}{\pi }$ .

Explanation of Solution

Given: $d=6\sin \left(2t\right)$

The equation of simple harmonic motion is given by,

  $y=a\cos \omega t$

And the given equation is,

  $d=6\sin \left(2t\right)$

The frequency is calculated as,

  $\begin{array}{c}f=\frac{1}{T}\\ =\frac{1}{\pi }\end{array}$

Therefore, the frequency is $\frac{1}{\pi }$ .