Question

This is the position graph of a mass on a spring. What can you say about the velocity and the force at the instant indicated by the dotted line? a) Velocity is positive; force is zero b) Velocity is negative; force is zero c) Velocity is negative; force is to the right. d) Velocity is zero; force is to the right. e) Velocity is zero; force is to the left. A

Answer 1

Answer: option D

The given system exhibits simple harmonic oscillation. In the given graph the displacement is sinusoidaliy varying. Here the maximum displacement is A. So we can represent the motion as :

displacement, x=A cos(wt) and

velocity, v= -Aw sin(wt). So the maximum velocity is Aw and when the displacement is maximum velocity will be zero.

At the given point displacement is maximum. So velocity will be zero.

Here the object vibrating is acted upon by a restoring force. This force is represented using Hooks law.

F= -kx, where k is the spring constant. This force causes the vibrating object to slow down as it go away. ie it will act in a direction opposite to the displacement. Here the displacement is in the negative direction. Therefore force will act towards positive direction. That means towards right. So the correct option is D.