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Question

The equation of a wave is y(x,t)=0.1sin[π3(10x30t)π6] m.
Find the acceleration of the particle at x=0.85 m and t=0.25 s
[Assume, π2=10 ; denotes positive ydirection and denotes negative ydirection ]

A
40 m/s2
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B
50 m/s2
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C
40 m/s2
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D
50 m/s2
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Solution

The correct option is B 50 m/s2
Given ,
Equation of the wave is
y(x,t)=0.1sin[π3(10x30t)π6] m

Differentiating twice on both sides with respect to time,

dydt=0.1cos[π3(10x30t)π6]×(10π)

d2ydt2=(π)sin[π3(10x30t)π6]×(+10π)

So, acceleration of particle d2ydt2=10π2sin[π3(10x30t)π6]

at x=0.85 m & t=0.25 sec we get ,

a=10π2sin[π3(8.57.5)π6]

a=10π2sin(π6)=50 m/s2
Thus, option (b) is the correct answer.

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