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Q.

The oscillation of a body on a smooth horizontal surface is represented by the equation,X=Acos⁡(ωt)where x = displacement at time tω=frequency of oscillationWhich one of the following graphs shows correctly the variation a with t?

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a

b

c

d

answer is C.

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Detailed Solution

Here, X=Acos⁡ωt∴  Velocity, v=dXdt=ddt(Acos⁡ωt)=−Aωsin⁡ωt Acceleration, a=dvdt=ddt(−Aωsin⁡ωt)=−Aω2cos⁡ωt Hence the variation of a with t is correctly shown by graph (c).
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