Chapter 15: Q1Q (page 434)

Which of the following describe for the SHM of Fig.:
(a) $- π < ϕ < - π / 2$ ,
(b) $π < ϕ < 3 π / 2$ ,
(c) $- 3 π / 2 < ϕ < - π$ ?

Short Answer

Expert verified

The limits which describes $ϕ$ for the SHM are $- π < ϕ < - \frac{π}{2} and π < ϕ < \frac{3 π}{2}$ .

Step by step solution

The given data

The graph of x versus t is given.

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, $X (t) = A \cos (ω t + ϕ)$ (i)

where, A is the maximum displacement, $ω$ is the angular velocity, t is time and $ϕ$ is the phase difference.

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:

$X = A \cos (ϕ)$

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 $- π < ϕ < - \frac{π}{2} and π < ϕ < \frac{3 π}{2}$ .

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Which of the following describe for the SHM of Fig.:
(a) $- π < ϕ < - π / 2$ ,
(b) $π < ϕ < 3 π / 2$ ,
(c) $- 3 π / 2 < ϕ < - π$ ?

Short Answer

Step by step solution

The given data

Understanding the concept of SHM of a particle

Calculation of the phase angle that describes the SHM

One App. One Place for Learning.

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Which of the following describe for the SHM of Fig.:(a) -π<ϕ<-π/2, (b) π<ϕ<3π/2,(c) -3π/2<ϕ<-π?

Short Answer

Step by step solution

The given data

Understanding the concept of SHM of a particle

Calculation of the phase angle that describes the SHM

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Physical Quantities And Units

Measurements

Medical Physics

Turning Points in Physics

Work Energy and Power

Atoms and Radioactivity

Study anywhere. Anytime. Across all devices.

Which of the following describe for the SHM of Fig.:
(a) $- π < ϕ < - π / 2$ ,
(b) $π < ϕ < 3 π / 2$ ,
(c) $- 3 π / 2 < ϕ < - π$ ?