Figure P13.23 shows another type of vibration absorber that uses mass, stiffness, and damping to reduce vibration. The damping can be used to reduce the amplitude of motion near resonance. The main mass is m1 and the absorber's mass is m2. Suppose the applied force f(t) is sinusoidal.
a. Derive the expressions for X1(j()/F (j() and X2(j()/F(j().
b. Use these expressions to discuss the selection of values for m2, k2, and c to minimize the motion of mass m1. To aid in your discussion, plot k1 X1 / F versus (/(k1/m1 for several values of ( = c/2(k1m1.