Question: The DGL for the spring-mass system with small deflections with friction is: mx (t)+rx`(t) +kx(t)=0 There is an oscillating spring-mass system with the following characteristics:

The DGL for the spring-mass system with small deflections with friction is:

mx" (t)+rx`(t) +kx(t)=0

There is an oscillating spring-mass system with the following characteristics:

Mass m = 1 kg. Friction factor: r = 5 kg / s and the spring constant k = 4 N / m.

a) Find the solution x = x (t) for the starting position x (0) = 0 and starting speed 2 m / s.

b) The system is now excited by the external force f (t) = 2(e)^at, t> or equal 0

(so-called forced oscillation). Find the general solutions of the oscillation equation for different values of a.

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