Question

what is the maximum value of pe is SHM

Answer 1

At extreme positions, the kinetic energy of a particle is zero. The particle is at rest at that moment. Since simple harmomic motion deals with forces that increase with separation (linearly for ideal cases of SHM), at extreme positions the system has the maximum potential energy. For SHM with ideal linear forces, the potential energy increases with the square of distance from the mean position.

Answer 2

Think about the energy changes in a mechanical oscillator. Recap that, as it passes through its equilibrium position, its speed and hence its kinetic energy are a maximum. At the maximum displacement, the speed and hence the kinetic energy are both zero. The potential energy will be a maximum when the speed is zero and vice versa. Assuming that there is no friction or air drag the total energy input E of the oscillator must remain constant

For the mass and spring system, the work done stretching a spring by an amount x is the area under the force extension graph = 1/2 kx2. The PE-extension graph is a parabola.

The kinetic energy will be zero at +A and a maximum when x = 0, so its graph is an inverted version of the strain energy graph. At any position kinetic + elastic strain energy is a constant E, where E = KEmax = PEmax.

PEmax µ A2, so the total energy E of SHM is proportional to (amplitude

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