An oscillator has a spring constant k, mass m, and a damping coefficient c.
a. write an equation of motion for this oscillator
c. For the rest of the problem take this to be a critically damped oscillator. Find the general solutions for x(t) and v(t) for the oscillator.
d. the oscillator is displaced ant a distance x0 and released from rest. Find the specific solutions for x(t) and v(t).
e. What is the initial energy put into the oscillator by displacing it? f. find the rate at which the energy is being lost due to damping as a function of time.
g. show that the total energy lost through damping balances the energy initially put into the system.
h. describe what happens if you try to drive this critcally damped oscillator. How does it respond? Can you achieve resonance?