Is it possible to express the total energy of a damped linear oscillator as a function of time? I'm confused here. I'd like to find E(t). As the oscillation is damped, dE/dt should everywhere be negative (energy being dissipated as radiation or heat). By setting E(t) equal to zero, shouldn't I be able to solve for the time at which the energy of the oscillating system is zero, and thus the time at which the system stops oscillating? And shouldn't this time be finite? Is there another way to find the time at which the damped oscillator will stop oscillating? Thanks!