1. ## 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.

2. ok. I think I noticed my problem I think that my U(t) should be Acost + Bsint, then go on to solve for A and B. Is this correct?