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Q. 16

Expert-verifiedFound in: Page 507

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 $d=5\mathrm{cos}\left(\frac{\pi}{2}t\right)$

(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 5

c) The period is 4

d) The frequency is $\frac{2}{\pi}$

Our given equation is $d=5\mathrm{cos}\left(\frac{\pi}{2}t\right)$

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

Comparing the equation with standard wave equation we get $a=5$

We get,

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

We have,

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

a) It is a simple harmonic motion

b) The amplitude is 5

c) The period is 4

d) The frequency is $\frac{2}{\pi}$

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