For a damped harmonic oscillator the displacement amplitude varies with time as

MATHEMATICS · Subjective · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

A(t)=A_0 e^{-kt}

, where

k

is a positive constant. (a) Show that the total mechanical energy

E(t)

of the oscillator can be written in the form

E(t)=E_0 e^{-2kt}

, where

E_0

is the initial energy. (b) State whether the energy decay is exponential, linear, or of some other form.