Question: Find the general solution to the following systems. Distinguish between the vibrational and unstable modes. What constraints on the initial conditions ensure that the unstable

Find the general solution to the following systems. Distinguish between the vibrational and unstable modes. What constraints on the initial conditions ensure that the unstable modes are not excited?
(a)

(b)

(c)

Find the general solution to the following systems. Distinguish between

(d)

d u it di2 d'v -2S d-u dz2 dv d'v D) dt 10 dt2 d-u d2u d w =--211 + 2 u_4w

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