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Question

Two simple harmonic motions are represented by the equations y1=0.1sin(100πt+π3) and y2=0.1cosπt. The phase difference of the velocity of particle 1 with respect to velocity of particle 2 at t=0 is

A
π6
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B
π3
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C
π3
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D
π6
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Solution

The correct option is C π6

y1=0.1sin(100πt+π3)

y2=0.1cosπt=0.1sin(π2+πt)=0.1sin(πt+π2)

Now, for finding velocity of particle , differentiate both equations with respect to time .

dy1dt=v1=0.1×100πcos(100πt+π3)

similarly for 2nd equation,

dy1dt=v2=0.1×πcos(πt+π2)=0.1πcos(πt+π2)

if equation x=Asin(ωt+ϕ) is given then, at t=0 phase of motion is ϕ

similarly at t=0 phas of 1st particle velocity is π3

at t=0 phase of velocity of 2nd particle is π2

now thw phase difference = phase of 1st particle at t=0 - phase of 2nd particle att=0

=π3π2=π6


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