A simple harmonic oscillator has total energy E that is equal to the sum of its kinetic energy and potential energy. The document shows that for a simple harmonic oscillator, the kinetic energy equals the potential energy when the displacement x equals A/√2, where A is the maximum amplitude. This is because the total energy equation is separated into kinetic and potential energy terms, and setting them equal provides the displacement where they are equal, which is A/√2.

1. Q: A simple harmonicoscillatorhasatotal energyE. At whatdisplacementdoeskineticenergyequal to
potential energyandwhy?
A: total energyof SHM= (1/2)kA2
=kineticenergy+potential energy
 Andkineticenergy=potential energy
 (1/2)kA2
=(2)potential energy
 Andpotential energy=(1/2)kx2
where x isdisplacement
 (1/2)kA2
=kx2
thenmultiply bothsides by2,cancel the k fromboth sides
 Displacement=x=A/sqrt2