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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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Most popular questions from this chapter

A particle executes linear SHM with frequency 0.25Hz about the point x=0. Att=0, it has displacement x=0.37cm and zero velocity. For the motion, determine the (a) period, (b) angular frequency, (c) amplitude, (d) displacement x(t), (e) velocity v(t), (f) maximum speed, (g) magnitude of the maximum acceleration, (h) displacement at t=3.0s, and (i) speed att=30s.

Although California is known for earthquakes, it has large regions dotted with precariously balanced rocks that would be easily toppled by even a mild earthquake. The rocks have stood this way for thousands of years, suggesting that major earthquakes have not occurred in those regions during that time. If an earthquake were to put such a rock into sinusoidal oscillation (parallel to the ground) with a frequency of2.2Hz, an oscillation amplitude of1.0cmwould cause the rock to topple. What would be the magnitude of the maximum acceleration of the oscillation, in terms of g?

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