An oscillator with mass 0.5 kg, stiffness 100 N/m, and mechanical resistance 1.4 kg/s is driven by a sinusoidal force of amplitude 2 N. Plot the speed amplitude and the phase angle between the displacement and speed as a function of the driving frequency and find the frequencies for which the phase angle for which the angle is 45 deg.
The Attempt at a Solution
Using the general form of the solution:
x(t) = A(w) sin(wt-Φ)
A(w) = (F/m)/((w_0^2-w^2)^2 + (2wp)^2)^0.5
I am positive the above equations are correct and come from the differential equation for this case.
Now, u(t) [speed] = d x(t)/dt.
My question: Now the speed amplitude, I believe, is wA(w). Won't the phase angle between the displacement and velocity always be pi/2 irrespective of w?