Question

A particle of mass \[m\] is hanging vertically by an ideal spring of force constant \[K\] . If the mass is made to oscillate vertically, its total energy is
A) Maximum at the extreme position
B) Maximum at the mean position
C) Minimum at the mean position
D) Same at all positions

Answer 1

Hint: When a spring is stretched beyond its original length, a force must be given to it; this force relies on the spring constant and the length to which it has been stretched. Due to the length's expansion, the force exerts some force. Here, the formula for the work generated by spring stretching must be applied. The square of the spring's increased length after stretching determines the amount of work that is done.

Complete step by step solution:
In order to know that simple harmonic motion is the motion of a particle moving in a straight line with an acceleration that is always directed towards a fixed point on the line and whose magnitude is proportional to the distance from the fixed point.

A restoring force that obeys Hooke's law tends to bring the system back to equilibrium when it has been moved from its equilibrium position. When a mass \[m\] is moved out of its equilibrium position, a net restoring force is applied to it. It then accelerates and begins to return to the equilibrium position as a result.

The restoring force decreases as the mass approaches the equilibrium position. The net restoring force disappears at the equilibrium position. Thus, the total energy remains constant at all positions in simple harmonic motion.

Therefore, the correct option is (D) Same at all positions

Note: It should be noted that the interaction of potential energy and kinetic energy is another aspect of simple harmonic motion. Potential energy is all stored energy, whether it is kept in stretched elastic materials or gravitational fields. One form of energy increases while the other decreases, but the total amount of energy does not change. Energy in a closed system neither creates nor destroys energy; it just transfers from one place to another, as demonstrated by the constant total energy.