1. Consider the spring-mass system: 0.1r" + 10x = 3 cos(wt), x(0) =0, r'(0) =0 (a) Solve for a(t) when w = 11. (b) Rewrite your answer using the trig identity: cos(B) - cos(A) = 2 sin (4-B ) sin( (AtB) (c) Sketch the graph of your solution. 2. Consider the spring-mass system (from Problem 1): 0.1x" + 10r = 3 cos(wt), x(0) =0, r'(0) =0 (a) For which value of w does resonance occur? (b) Solve for a(t) using your value of w from (a). (c) Sketch the graph of your solution. 3. A 6-kg mass is attached to a spring with spring constant & = 6 N/m. Suppose the system is immersed in a medium with damping coefficient c = 8 N-s/m and an external force F(t) = 8 cos(wt) N acts on the system. (a) Find the steady-state solution To when w = 3 and identify the amplitude C(3). (b) Identify the practical resonance frequency max. (c) Identify the practical resonance amplitude C(wmax)