Physics
Physics
Problem
A block of mass 250 g executes simple harmonic motion with angular frequency 8 rad s⁻¹. If its total mechanical energy is 0.50 J, calculate the amplitude of oscillation.Intuitive explanation
Simple harmonic motion stores energy in two forms—kinetic and potential—that trade back and forth, but their sum stays constant. The key insight is that all the mechanical energy converts to potential energy at maximum displacement (the amplitude), where the block momentarily stops. Use the potential energy formula for a spring-like restoring force to connect total energy directly to amplitude.
Intuitive explanation
Simple harmonic motion stores energy in two forms—kinetic and potential—that trade back and forth, but their sum stays constant. The key insight is that all the mechanical energy converts to potential energy at maximum displacement (the amplitude), where the block momentarily stops. Use the potential energy formula for a spring-like restoring force to connect total energy directly to amplitude.