Q2 [20 pts] A delicate instrument of mass M2 = 10 kg contained in a box...

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Q2 [20 pts] A delicate instrument of mass M2 = 10 kg contained in a box M = 5 kg is to be isolated from external sinusoidal vibration b(t) = 0.1sin20t m as illustrated in the figure. y2(t) m FW M2 K2 M1 K1 Base C1 y(t) Yb(t) a. (5 pts) Assume there are no spring k and damper C (in other words, M2 sits on M1). Design an undamped isolator (in other words, find k) such that the transmitted displacement is 15% of the base motion and calculate the transmitted force. b. (5 pts) Change the design of an undamped isolator in (a) by adding a viscous damper (in other words, find c) with damping ratio ( chosen such that the transmitted displacement at resonance is 200 % of the base motion. c. (10 pts) Now, assume you put a spring k2 and a damper C2 which have same value of k and C1. Derive the equation of motion of the system in matrix form. Q2 [20 pts] A delicate instrument of mass M2 = 10 kg contained in a box M = 5 kg is to be isolated from external sinusoidal vibration b(t) = 0.1sin20t m as illustrated in the figure. y2(t) m FW M2 K2 M1 K1 Base C1 y(t) Yb(t) a. (5 pts) Assume there are no spring k and damper C (in other words, M2 sits on M1). Design an undamped isolator (in other words, find k) such that the transmitted displacement is 15% of the base motion and calculate the transmitted force. b. (5 pts) Change the design of an undamped isolator in (a) by adding a viscous damper (in other words, find c) with damping ratio ( chosen such that the transmitted displacement at resonance is 200 % of the base motion. c. (10 pts) Now, assume you put a spring k2 and a damper C2 which have same value of k and C1. Derive the equation of motion of the system in matrix form.