Physics
Physics
Problem
Answer the following questions related to the energy aspects of simple harmonic motion. a. (i) Explain why the total mechanical energy of a particle executing simple harmonic motion remains constant even though both kinetic and potential energies vary with time. b. (ii) Show qualitatively how the total mechanical energy of the particle depends on the amplitude of oscillation. c. (iii) Draw (no scale needed) and label the graphs of kinetic energy and potential energy versus displacement for one complete oscillation, indicating clearly the points where each energy is maximum and minimum. d. (iv) Using the energy–displacement relationship, explain why the speed of the particle is zero at the extreme positions and maximum at the mean position.Intuitive explanation
Simple harmonic motion is fundamentally about energy trading back and forth between two forms—kinetic and potential—while their sum stays constant. The key insight is that at any position, you can find how fast the object is moving (or how much potential energy it has stored) by using energy conservation: total energy equals the sum of kinetic and potential at every instant. Understanding where the object has maximum speed versus maximum displacement unlocks most SHM energy problems.
Intuitive explanation
Simple harmonic motion is fundamentally about energy trading back and forth between two forms—kinetic and potential—while their sum stays constant. The key insight is that at any position, you can find how fast the object is moving (or how much potential energy it has stored) by using energy conservation: total energy equals the sum of kinetic and potential at every instant. Understanding where the object has maximum speed versus maximum displacement unlocks most SHM energy problems.