The oscillation of a body on a smooth horizontal surface is represented by the equation,

              X = A cos (\omegat)

Where    X = displacement at time t

             \omega = frequency of oscillation

Which one of the following graphs shows correctly the variation 'a' with 't'?

Here a = acceleration at time t

        T = time period

  • Option 1)

  • Option 2)

  • Option 3)

  • Option 4)

 

Answers (1)

Given x=A\cos wt

Velocity v=\frac{dx}{dt}= -Aw \sin\left ( wt \right )

Acceleration a=\frac{dv}{dt}=-Aw^{2}\cos \left ( wt \right )

Hence graph (3) correctlt dipities the variation of a with it.


Option 1)

Incorrect option

Option 2)

Incorrect option

Option 3)

Correct option

Option 4)

Incorrect option

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