A forced damped oscillator of mass m has a displacement varying with time given

Question

A forced damped oscillator of mass m has a displacement varying with time given by: x = A sin( ) The resistive force is -bv. From this information calculate how much work is done against the resistive force during one cycle of oscillation. For a driving frequency omega less than the natural frequency sketch graphs of potential energy, kinetic energy, and total energy for the oscillator over one complete cycle. Be sure to label important turning points and intersections with their values of energy and time.

Explanation / Answer

Well, here we need to calculate the work done for one cycle.
Angular frequency is given as ;
so the time required to complete one cycle is 2/;

Work done is the integral of Fdx;
here x is a function of time, hence the integral will from t = 0 to t = 2/.

b) Potential energy = mgx, so it will also varry with time;
and kinetic potential = 0.5*mv2 which is again a function of time;
and total energy is simply the sum of P.E. and K.E.

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