Please Whole Questions Able Whole Thing Part 3 4 Priority Answer Thanks Q29663913

Please do the whole questions but if not able to do the wholething so part 3&4 are the priority to answerThanks
Consider the vibrations of a mass-spring underdamped system when an extemal force is applied dt dt 1. Show that the damped oscillation (solution of the corresponding homogeneous equation) is given by -(b/2m 4mk-b2 2. Show that the steady-state solution (particular solution) is such that: my)cos(yt)+bysin 3. Show that the displacement from equilibrium of the mass at time t is given by 4. Use the above model to determine the steady state solution if a 64 lb weight is attached to a vertical spring, causing it to stretch 3 in. upon coming to rest at equilibrium. The damping constant for the system is 3 lb-sec/ft and an external force F(t)3 cos12t is applied to the weight. Show transcribed image text