Hi, we are using book : John Robert Taylor - Classical mechanics (2005, University Science Books)! Please show me all your works and explanations. I will appreciate with good review!!! Thank you in advance :)

Consider a weakly damped oscillator without a driving force, as discussed in Chapter 5 of Taylor. Suppose i(0) = 0 and x(0) = x0. Using "power equals force times velocity," and considering the time interval from zero to infinity, set up integrals and evaluate them to find (a the total work done by the spring on the particle. (b) the total work done by the frictional force on the particle. This should be negative. (c) How do your answers to parts (a) and (b) relate to the initial and final values of the spring potential energy and the initial and final kinetic energies of the particle