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Chapter 8: Q. 15 (page 507)

The displacement d (in meters) of an object at time t (in seconds) is given d=6cos(蟺t)

(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?

Short Answer

Expert verified

a) It is a simple harmonic motion

b) The amplitude is 6

c) The period is 2

d) The frequency is1蟺

Step by step solution

01

Given information

Our given equation isd=6cos(蟺t)

02

Part (a) Step 1: Explanation

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

03

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

Comparing the equation with standard wave equation we geta=6

04

Part (c) Step 1: Find period

We get,

蝇=2蟺T蟺=2蟺TT=2

05

Part (d) Step 1: Find the frequency

We get,

f=1蝇f=1蟺

06

Conclusion

a) It is a simple harmonic motion

b) The amplitude is 6

c) The period is 2

d) The frequency is1蟺

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