Question

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

X = Acos(ωt)

Where, X = displacement at time t

ω = frequency of oscillation

Which one of the following graph shows correctly the variation of a with t?

Here, a = acceleration at time t

T = time period.

Answer 1

As x = A cos ωt

∴ v = \(\frac{dx}{dt}\) = -Aω sinωt ........(i)

and, a = \(\frac{d^2x}{dt^2}\) = -Aω² cos ωt .........(ii)

We can find the correct graph by putting different values of t in Eq. (ii),

At, t = 0, a = -Aω²