The input, u(t), is a step function. State 1: m1= 0.5 m2=2 b1= b2 = 0.5 k1= k2= k3= 5 State 2: m1 = 0.5 m2 = 2 b1 = b2 = 5 k1 k2 k3= 5 b u(t) ww m ww k 2 m K2 (a) Derive the motion equations for the interconnected mass-spring-damper system. Express the system dynamics in 1. differential equations, 2. transfer functions (where positions are the outputs). (b)Graph the force magnitude resulting from the stretching and compression of spring k3. (c)Verbally describe when the movement of the two masses can be separated without altering the system's overall structure.