Calculating Velocity in Simple Harmonic Motion: A Pendulum Clock Analogy

[jatin1990]

Homework Statement

Speed of particle executing simple harmonic motion with amplitude A is half of the maximum speed. At that instant, displacement of the particle is ?

Homework Equations

The Attempt at a Solution

 

[gash789]

You have worded this question somewhat strangely but I will attempt a solution. Think of the particle under SHM as a Pendulum clock (or weight on the end of a string). If it is "ticking" then ask "what is the velocity" at these two points:

1) When it is at maximum displacement from the vertical

2) When it passes through the vertical displacement.To give a full answer one could consider its energy. The total energy is a sum of the Kinetic and Potential energy, these must always be conserved. At the maximum displacement it changes direction, therefore at some instant it must speed=0.

At the point it passes through the vertical it is the "lowest" point, so will have the minimum potential energy. Therefore it must have the maximum kinetic energy, hence maximum velocity. Therefore you must only work out where it will have half this value.