Find the expression for kinetic energy, potential energy and total energy in simple harmonic motion. Show the variation of kinetic energy, potential energy and total energy with (i) time and (ii) displacement graphically.

Find the expression for kinetic energy, potential energy and total ene

1.	Find the expression for kinetic energy, potential energy and total energy in simple harmonic motion. Show the variation of kinetic energy, potential energy and total energy with (i) time and (ii) displacement graphically.
Answer» Solution :The displacement is `x=acosomegat`, this means that the MOTION starts at one end of the path, comes to the MEAN position at `T/4` (T = time period), goes to the other end at `T/2`, then again comes to the mean position at `(3T)/4`, and FINALLY comes back to the starting point at time T, thus completing a COMPLETE oscillation. The variation of the KE, the PE and the total energy (i) with time t is shown in the graph of Fig. 1.44(a), (ii) with displacement x is shown in the graph of Fig. 1.44(b).