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The oscillationof a body on a smooth hor...

The oscillationof a body on a smooth horizontal surface is represented by the equation
`x=Acos omegat`
where `x=` displacement at time t, `omega=` frequency of oscillation. Which one of the following graphs shows correctly the variation of acceleration a with time t ?

A

B

C

D

Text Solution

Verified by Experts

The correct Answer is:
C
Acceleration, `a = (d^(2)X)/(dt^(2)) = (d^(2))/(dt^(2))(A cos omegat)`
`a = -Aomega^(2) cos omegat`
`t = 0, a = -Aomega^(2)`
At `t = (T)/(2), a = -omega^(2) cos omega xx (T)/(2) = -Aomega^(2) cos pi`
` = + A omega^(2)`
At ` t = T, a = -omega^(2) cos ((2pi)/(T) xx T) = -Aomega^(2)`
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