Concept:In Simple Harmonic Motion (SHM), the total mechanical energy is conserved, constantly shifting back and forth between kinetic (motion) and potential (position) forms.
Formula:$$ PE = \frac{1}{2} k x^2 $$
$$ KE = \frac{1}{2} m v^2 $$
Solution:- At the mean position (equilibrium, \( x = 0 \)), the restoring force is zero, meaning potential energy is minimum. Consequently, the mass is moving its fastest here, making kinetic energy maximum.
- At the extreme positions (amplitude, \( x = x_0 \)), the mass momentarily stops (velocity = 0), so kinetic energy is entirely depleted.
- Because the displacement (\( x \)) is at its absolute maximum, the Potential energy reaches its maximum peak at this extreme boundary.
Why other options are incorrect:Kinetic energy is zero, not maximum, at the extreme positions (Option A). At the mean position, KE is maximum, not minimum (Option C/D).
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