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Chapter 8: Q. 16 (page 507)

The displacement d (in meters) of an object at time t (in seconds) is given d=5cos(蟺2t)

(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 5

c) The period is 4

d) The frequency is 2蟺

Step by step solution

01

Given information

Our given equation isd=5cos(蟺2t)

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

Comparing the equation with standard wave equation we geta=5

04

Part (c) Step 1:  Find period 

We get,

蝇=2蟺T蟺2=2蟺TT=4

05

Part (d) Step 1: Find frequency

We have,

f=1蝇f=2蟺

06

Conclusion

a) It is a simple harmonic motion

b) The amplitude is 5

c) The period is 4

d) The frequency is2蟺

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