In real physical systems there is always some damping (i. e. gamma > 0), from fr

Question

In real physical systems there is always some damping (i. e. gamma > 0), from frictional effects if nothing else. Show that where xh(t) is the homogeneous solution of the equation . [Thus, xh(t) is a transient solution - one that dies out with the passage of time, leaving only the particular solution xp(t), called the steady state solution. ] Find the transient motion and steady state oscillations of a damped mass-spring system with m = 1, gamma = 2, and k = 12 under the influence of an external force F(t) = 18cos(2t) with x(0) = 3 and x(0) = 0.

Explanation / Answer

Mass (m) is attached to Hook

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