A mass spring damper system is acted upon by this periodic force: F = F1 cos (At) + F2cos(At/B) , B > 1, where F1, F2, A, and B are parameters that have been given. What effect does (a) change in mass, (b) change in stiffness, (c) change in damping coefficient have on the force transmitted to the support.

weight .) A weight of 64 pounds (Recall mx" + Bx' + kx stretches a spring 2 feet. A damping device imparts a damping force 0 and m 32 numerically equal to 16 times the instantaneous velocity. The initial position is x (0) = 2 and the initial velocity is x' (0) = –1 . This is the equation of motion for the mass. -4t x = (-2t – 1) e t -4t O x = (-7t – 2) eAt -2t O x = 2e cos(2t) +e t sin(2t) -4t O x = (7t + 2) e

A 3-kg mass is attached to a spring with stiffness 60 N/m. The damping constant for the system is 12√5 N-sec/m. If the mass is pulled 20 cm to the right of equilibrium and given an initial rightward velocity of 4 m/sec, what is the maximum displacement from equilibrium that it will attain?

Near the top of the Citigroup Center building in New York City, there is an object with mass of 3.8 × 105 kg on springs that have adjustable force constants. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven—the driving force is transferred to the object, which oscillates instead of the entire building. a)What effective force constant should the springs have to make them oscillate with a period of 1.4 s in N/m? b)What energy is stored in the springs for a 1.8 m displacement from equilibrium in J?