I have this problem any help would be greatly apprecited! then, In the mass-spri

Question

I have this problem any help would be greatly apprecited!

then,

In the mass-spring system below, we have m1 = 2 kg, m2 = 1 kg, and the spring con¬stants are k1 = k2 = 2 and k3 = 1 kg/sec2. Find the general solution for the displacements x1(t) and x2(t) of the two masses relative to their equilibrium positions. Repeat the previous problem assuming there is an external oscillating force F(t) = 40 cos omega t acting on the second mass (and 0 external force on the first). [Hint: Use Undetermined Coefficient to find a particular solution of the nonhomogeneous system.]

Explanation / Answer

x1=A1e^iw1t

x2=A2e^iw2t

then we get

w1=sqrt(k1+k2)/m1

w1=sqrt(2)

w2=3

x1(t)=A1e^i(sqrt(2))t

x2(t)=A2e^i3t

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