How will the elastic potential energy and the gravitational potential energy change at different points in the oscillation?

To understand how elastic potential energy and gravitational potential energy change at different points in the oscillation, we need to consider a simple harmonic oscillator, such as a mass-spring system.

In a mass-spring system, a mass is attached to a spring, and when the mass is displaced from its equilibrium position, it experiences a restoring force due to the spring. This restoring force causes the mass to oscillate back and forth around the equilibrium position.

Let's consider different points in the oscillation:

1. Maximum displacement: At the maximum displacement from the equilibrium position, the spring is stretched or compressed to its maximum extent. At this point, the elastic potential energy is at its maximum because the spring is storing the maximum amount of potential energy due to its deformation. The gravitational potential energy is at its minimum since the height of the mass is minimal.

2. Equilibrium position: At the equilibrium position, the spring is neither stretched nor compressed. Therefore, the elastic potential energy is zero because the spring is not deformed. The gravitational potential energy is also zero since the height of the mass is minimal.

3. Maximum displacement in the opposite direction: Similar to the first case, at the maximum displacement in the opposite direction, the spring is stretched or compressed to its maximum extent, but in the opposite direction. The elastic potential energy is again at its maximum, but with opposite sign. The gravitational potential energy is still at a minimum since the height of the mass is minimal.

In summary, as the mass oscillates in a mass-spring system, the elastic potential energy varies, reaching maximum at the maximum displacement positions, and zero at the equilibrium position. On the other hand, the gravitational potential energy remains constant, reaching minimum at the maximum displacement positions, and zero at the equilibrium position.