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Chapter 15: Q1Q (page 434)

Which of the following describe for the SHM of Fig.:

(a) -蟺<蠒<-蟺/2,

(b) 蟺<蠒<3蟺/2,

(c) -3蟺/2<蠒<-蟺?

Short Answer

Expert verified

The limits which describes 蠒for the SHM are -蟺<蠒<-蟺2and蟺<蠒<3蟺2.

Step by step solution

01

The given data 

The graph of x versus t is given.

02

Understanding the concept of SHM of a particle

We can use the displacement of SHM to find the expression for X at t = 0. Then, by observing the graph we can interpret the possible values of the phase angle.

Formula:

The displacement equation of a particle in motion,X(t)=Acos(蝇t+蠒) (i)

where, A is the maximum displacement, 蝇is the angular velocity, t is time and 蠒is the phase difference.

03

Calculation of the phase angle that describes the SHM

At t = 0 we get, we can get the displacement of the particle using equation (i) as follows:

X=Acos(蠒)

From the graph, we can see that at t = 0 the value of X is negative; we know that the value of cosine function is negative in II and III quadrant.

Hence, the limits of the phase are -蟺<蠒<-蟺2and蟺<蠒<3蟺2.

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When a 20 Ncan is hung from the bottom of a vertical spring, it causes the spring to stretch 20 cm .

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