Find the real-valued velocity response vt dxdt is the

Question

A spring-mass-damper system is driven by a triangular wave forcing function as described by the equation: mx^.. + Rx^. + S_cx, where

f(t) = A8/Π² ∑_n=1^∞ (-1)ⁿ/ (2n-1)² sin(ω1[2n-1]t)

See the waveform sketch below. Hint: You know the frequency-dependent mechanical impedance of a mass-spring-damper system, and you know that superposition applies.

(a.) Find the real-valued velocity response v(t) = dx/dt.

(b.) Is the output v(t) also a triangular wave? Explain briefly.

(c.) What is the mean square velocity v^2.

(d.) Find the average power W dissipated per cycle.