Question

Derive expressions for the kinetic energy and potential energy of a simple harmonic oscillator.

Answer 1

Derive an expression for kinetic andpotential energies of a simple harmonic oscillators. Hence show that total energy is conserved in simple harmonic motion.In which position of the oscillators is the energy wholykinetic or potential

Answer 2

Hey mate,

◆ Explained Answer-
Consider a particle of mass m moving in SHM.
The position of particle is given by-
x = Asin(ωt+δ)

Now, we can configure velocity,
v = dx/dt
v = Aωcos(ωt+δ)

a) Kinetic energy is
K.E. = 1/2 mv^2
K.E. = 1/2 m [Aωcos(ωt+δ)]^2
K.E. = 1/2 m A^2 ω^2 cos^2(ωt+δ)

b) Potential energy is
P.E. = 1/2 kx^2
P.E. = 1/2 m ω^2 [Asin(ωt+δ)]^2
P.E. = 1/2 m A^2 ω^2 sin^2(ωt+δ)

Hope this helps you...