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Q. 15

Expert-verified
Found in: Page 507

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

c) The period is 2

d) The frequency is $\frac{1}{\pi }$

See the step by step solution

Step 1: Given information

Our given equation is $d=6\mathrm{cos}\left(\pi t\right)$

Part (a) Step 1: Explanation

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

Part (b) Step 1: The maximum displacement of object from resting position is the amplitude

Comparing the equation with standard wave equation we get $a=6$

Part (c) Step 1: Find period

We get,

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

Part (d) Step 1: Find the frequency

We get,

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

Step 6: Conclusion

a) It is a simple harmonic motion

b) The amplitude is 6

c) The period is $2$

d) The frequency is $\frac{1}{\pi }$