Perhaps surprisingly, we can apply the transfer-function

Chapter 6, Problem P6.35

(choose chapter or problem)

Perhaps surprisingly, we can apply the transfer-function concept to mechanical systems. Suppose we have a mass m moving through a liquid with an applied force f and velocity v. The motion of the mass is described by the first-order differential equation f = m dv dt + kv in which k is the coefficient of viscous friction. Find an expression for the transfer function H(f) = V F Also, find the half-power frequency (defined as the frequency at which the transfer function magnitude is 1/ 2 times its dc value) in terms of k and m. [Hint: To determine the 338 Chapter 6 Frequency Response, Bode Plots, and Resonance transfer function, assume a steady-state sinusoidal velocity v = Vm cos(2ft), solve for the force, and take the ratio of their phasors.