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Q. 17

Expert-verified
Found in: Page 550

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# The displacement d (in meters) of an object at time t (in seconds) is given $d=-3\mathrm{sin}\left(\frac{1}{2}t\right)$(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?

a) It is a simple harmonic motion

b) The amplitude is -3

c) The period is $\pi$

d) The frequency is 2

See the step by step solution

## Step 1: Given information

We are given an equation $d=-3\mathrm{sin}\left(\frac{1}{2}t\right)$

## Part (a) Step 1: Explanation

As the object is modeled by sine function the given wave is simple harmonic.

## Part (b) Step1: The maximum displacement of object from resting position is the amplitude

Comparing the equation with standard wave equation we get $a=-3$

## Part (c) Step 1: Find period

We get,

$\omega =\frac{2\pi }{T}\phantom{\rule{0ex}{0ex}}\frac{1}{2}=\frac{2\pi }{T}\phantom{\rule{0ex}{0ex}}T=4\pi$

## Part (d) Step 1: Find frequency

We get,

$f=\frac{1}{\omega }\phantom{\rule{0ex}{0ex}}f=2$

## Step 6: Conclusion

a) It is a simple harmonic motion

b) The amplitude is 5

c) The period is $\pi$

d) The frequency is 2