Chapter 5.6, Problem 35E

To determine

To find: The equation of the motion of the mass.

Answer to Problem 35E

The equation of the motion of the massis $d\left(t\right)=5\cos \left(2\pi t\right)$

Explanation of Solution

Given Information:

The amplitude of the motion is $5\text{cm}$ and the time period is $1\text{s}$ . the displacement is maximum at $t=0$ .

Concept used:

The standard form of the simple harmonic motion when the displacement is maximum at $t=0$ is given by,

  $y=A\cos \omega t$

The angular velocity is given by:

  $\omega =\frac{2\pi }{T}$

The function of the simple harmonic motion in time period term is given by,

  $y=A\cos \left(\frac{2\pi t}{T}\right)$

The equation of the motion of the massis calculated as,

  $\begin{array}{c}d\left(t\right)=a\cos \left(\frac{2\pi t}{T}\right)\\ =5\cos \left(\frac{2\pi t}{1}\right)\\ =5\cos \left(2\pi t\right)\end{array}$

Thus, the equation of the motion of the massis $d\left(t\right)=5\cos \left(2\pi t\right)$ .