Problem

Problems deal with a nuiss−spring−dashpot system having position function x(t) satisfying...

Problems deal with a nuiss−spring−dashpot system having position function x(t) satisfying Eq. (4). We write x0 = x(0) and v0 = x′(0) and recall that p = c/(2m), ω02 = k/m, and ω12 = ω02 − p2. The system is criticallydamped, overdamped, or underdamped, as specified in each problem.

Critically damped) Show in this case that

x(t) = (x0 + v0t + px0t)e−pt.

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Solutions For Problems in Chapter 2.4