Question

Total energy of a pendulum performing simple harmonic motion is

• A. Same at every point
• B. Maximum at extreme points
• C. Maximum at mean position
• D. Minimum at mean position

Answer 1

Answer:

A. Same at every point

• Definition: The total mechanical energy (E) of a simple pendulum performing Simple Harmonic Motion (SHM) is the sum of its kinetic energy (K) and potential energy (U).
• Conservation Principle: In an ideal system without friction or air resistance, the total energy remains constant at any point in the oscillation path. This is a consequence of the Law of Conservation of Mechanical Energy.
• Energy Components:
  • Kinetic Energy (K): Maximum at the mean position (center) where velocity is highest and zero at the extreme positions.
  • Potential Energy (U): Maximum at the extreme positions where the pendulum reaches its greatest vertical displacement (height) and zero at the mean position.
• Mathematical Expression: The total energy is proportional to the square of the amplitude (A) of oscillation. It is defined as E = 1/2 * k * A^2, where 'k' is the force constant.
• Key Characteristics:
  • It is independent of time and displacement from the equilibrium position.
  • If damping forces like air resistance are present, the total energy of the pendulum decreases over time, leading to damped harmonic motion.
  • The energy conversion continuously oscillates between potential and kinetic forms as the pendulum moves, but the sum remains invariant in SHM.