Question

The oscillation of a body on a smooth horizontal
surface is represented by the equation, x = Acos(ot),
where x is displacement at time t and w is frequency
of oscillation. Which one of the following graphs
shows correctly the variation a with t?​

Answer 1

Answer:

Given:

An Oscillatory body has Equation of motion as follows :

x = A cos(ωt)

To find:

Graph which correctly represents it's acceleration vs Time relationship.

Concept:

Since we have displacement vs Time relationship, we can easily double differentiate the Equation to get acceleration vs Time relationship.

Calculation:

∴ x = A cos(ωt)

=> v = dx/dt = A [d{cos(ωt)}/dt]

=> v = - Aω sin(ωt)

=> acc. = dv/dt

=> acc. = - Aω² cos(ωt)

So, this is the acceleration vs Time relationship.

Now look at the attached photo to understand better.