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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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