Physics
Physics
Problem
A particle performs simple harmonic motion with amplitude and angular frequency . (a) For what magnitude of displacement from the equilibrium position will the kinetic energy be equal to the potential energy? (b) Calculate the speed of the particle when it is at this displacement.Intuitive explanation
In simple harmonic motion, energy constantly trades between kinetic and potential forms, but the total stays constant. The key insight is that when kinetic energy equals potential energy, each must be half the total mechanical energy—so you can use energy conservation to find the displacement, then use that to find the speed. Think of it as finding the "balance point" where the particle has split its energy equally between motion and position.
Intuitive explanation
In simple harmonic motion, energy constantly trades between kinetic and potential forms, but the total stays constant. The key insight is that when kinetic energy equals potential energy, each must be half the total mechanical energy—so you can use energy conservation to find the displacement, then use that to find the speed. Think of it as finding the "balance point" where the particle has split its energy equally between motion and position.