Ok here's the question: A body m is attached to a spring with spring constant k. While the body executes oscillations it also experiences a damping force F = -βv where 'v' is time derivative of displacement of the body from its equilibrium position. I believe equation of motion is F = m*d^2x/dt^2 + kx + β*dx/dt. (i) Let us completely ignore the damping term F = -βv. Assuming that the initial displacement is x0 and the initial velocity is 0, write down the expressions for x(t) and velocity as function of time. I'm confused here because it says to completely ignore the damping term? In which case wouldn't the mass just function as an undamped oscillator where x(t) = Acos(ωt) and v(t) = -ωAsin(ωt)? (ii) Now let us assume that the damping coefficient 'β' is non zero but very small, so that over one period of oscillation we may take x(t) and v(t) to be of the same form found in part (i) above. With this assumption, find the work done by the damping force during one time period of oscillation. Express your answer in terms of k, m, x0, and β. I think the integral of the force with respect to the x variable would give the work done for that force? So i'de get -βvx0 = W? And now i'm lost, I don't think the equations I wrote in (ii) are correct since the variables have nothing to do with this part. Any help appreciated thanks.