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## Homework Statement

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.

## Homework Equations

## The Attempt at a Solution

Using the general form of the solution:

x(t) = A(w) sin(wt-Φ)

where Φ=atan(2wp/(w_0^2-w^2))

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.

= w*A(w)*cos(wt-Φ)

=w*A(w)*sin(wt-Φ+pi/2)

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?

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