Chapter 8.5, Problem 15AYU

In Problems 13-20, the displacement $d$ (in meters) of an object at time $t$ (in seconds) is given.

(a) Describe the motion of the object.

(b) What is the maximum displacement from its resting position?

(c) What is the time required for one oscillation?

(d) What is the frequency?

$d=6\cos (\pi t)$

To determine

To find:

a. Motion of the object

b. Maximum displacement from its resting position

c. What is the time required for one oscillation?

d. What is the frequency?

Answer to Problem 15AYU

a. $\text{Motion} \text{of} \text{the} \text{object}=\text{Simple} \text{harmonic} \text{motion}$

b. $\text{Maximum} \text{displacement} = 6m$

c. $\text{T} = 2\sec$

d. $\text{f} = \frac{1}{2}\text{Hz}$

Explanation of Solution

Given:

$d = 6\text{cos}\left(\pi t\right)$

Formula used:

$d = a\text{cos}wt$

Calculation:

a. $\text{Motion} \text{of} \text{the} \text{object}=\text{Simple} \text{harmonic} \text{motion}$

b. $\text{Maximum} \text{displacement} \left|a\right| = 6m$

c. Period $\text{T} = \frac{2\text{π}}{\text{w}} = \frac{2\text{π}}{\text{π}} = 2$ sec

d. Frequency $f = \frac{1}{\text{T}} = \frac{1}{2}\text{Hz}$