Chapter 8.5, Problem 16AYU

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 16AYU

Solutions:

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

b. $\text{Maximum} \text{displacement} = 5m$

c. $\text{T} = 4\text{sec}$

d. $\text{f} = \frac{1}{4}$Hz

Explanation of Solution

Given:

$d = 5\text{cos}(\frac{\text{Π}}{2}\text{t})$

Formula used:

$d = a\text{cos}wt$

Calculation:

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

b. $\text{Maximum} \text{displacement} \left|a\right| = 5m$

c. Period $\text{T} = \frac{2\text{π}}{\text{w}} = \frac{2\text{π}}{\text{π}/2} = 4$ sec

d. Frequency $f = \frac{1}{\text{T}} = \frac{1}{4}\text{Hz}$