damped vibration problem.

Assume that the gravitational acceleration is g = 10 m/sec^2. A mass of 2 kg stretches an elastic spring 10m. The mass is also attached to a viscous damper with a damping constant of 1 N sec/m. Then the system is driven by an external force of (3cost + 2sint) N.

a) What is the equation of motion for the spring mass system?

b) Determine the steady state response U(t)

c) Express U(t) in the form R cos(wt - delta).

d) What is the quadrant of delta?

Ok. so I have: m= 2 kg

L= 10 m

F(t) = (3cost + 2sint)

k= 1 N sec/m

so 2u'' + u = (3cost + 2sint)

complementary solution: r^2 + 1/2 = 0

r = + or - 1/(sq rt 2) i

so for a) i got

u(t) = c1 cos[1/sq rt 2]t + c2 sin[1/sq rt 2]t

so U(t) = At cos[1/sq rt2]t + Bt sin[1/sq rt 2]t

Just wondering if I have this set up right so far, cause I had a little trouble solving for A when I got down to the end. Any problems you see or help would be greatly appreciated. Thanks.