MMAN2300 Problem Solving Exercise #9

(a) Draw a free-body diagram of the mass in the system illustrated at right.

Assume the motion of the massless base is given by tiYety )( .

(b) Find the equation of motion for the mass.

(c) Use the equation of motion to determine the magnitude of the transfer

function g()=X/Y .

(d) Let m = 10 kg, k1 = 400 N/m, c = 14.14 Ns/m, and k2 = 100 N/m. Find the natural

frequency of the system.

(e) Find the amplitude of the displacement of the mass if Y = 10 cm and = 5 rad/s.

Optional (not for marks):

(f) Find the amplitude of the force transmitted to the ceiling.

(g) Find the amplitude of the force acting on the base.