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Chapter 15: Q12Q (page 435)

Figure 15-29gives, for three situations, the displacements of a pair of simple harmonic oscillators (A and B) that are identical except for phase. For each pair, what phase shift (in radians and in degrees) is needed to shift the curve for A to coincide with the curve for B? Of the many possible answers, choose the shift with the smallest absolute magnitude.

Short Answer

Expert verified

a) Phase shift needed for A to coincide with B for curve (a) is 蟺rad or 180掳.

b) Phase shift needed for A to coincide with B for curve (b) is 蟺2or 90掳.

c) Phase shift needed for A to coincide with B for curve (c) is -蟺2rad or -90掳.

Step by step solution

01

The given data 

From the problem figure 15-29 is the graphs of x versus t.

02

Understanding the concept of the phase shift

We observe the given graphs and we can see the positions of curve A for B. Then we can determine by how many angles should the curve needs to shift to coincide with B.

03

Calculation of phase shift for curve (a)

a)

In graph (a) A and B have opposite phase, so for curve A needs to shift by 蟺rador180掳 to coincide with B.

04

Calculation of phase shift for curve (b)

b)

In graph (b) curve A lags behind curve B by 蟺2radians, therefore curve A needs to shift by 蟺2rad or90掳 to coincide with B.

05

Calculation of phase shift for curve (c)

c)

In graph (c) curve A leads curve B by 蟺2rad, therefore curve A needs to shift by -蟺2rador-90掳to coincide with B.

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Most popular questions from this chapter

A simple harmonic oscillator consists of a 0.50 kgblock attached to a spring. The block slides back and forth along a straight line on a frictionless surface with equilibrium point x=0. At t=0the block is at x=0and moving in the positive x direction. A graph of the magnitude of the net forceF鈫�on the block as a function of its position is shown in Fig. 15-55. The vertical scale is set by FS=75.0N. What are (a) the amplitude and (b) the period of the motion, (c) the magnitude of the maximum acceleration, and (d) the maximum kinetic energy?

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A block is in SHM on the end of a spring, with position given by x=xmcos(蝇t+蠒). If蠒=蟺/5rad, then at t = 0what percentage of the total mechanical energy is potential energy?

You are to complete Figure 15-22a so that it is a plot of velocity v versus time t for the spring鈥揵lock oscillator that is shown in Figure 15-22b for t=0. (a) In Fig.15-22a, at which lettered point or in what region between the points should the (vertical) v axis intersect the t axis? (For example, should it intersect at point A, or maybe in the region between points A and B?) (b) If the block鈥檚 velocity is given byv=-vmsin(蝇t+蠒), what is the value of蠒? Make it positive, and if you cannot specify the value (such as+蟺/2rad), then give a range of values (such as between 0 and蟺/2rad).

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