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.
(Underdamped) If the damping constant c is small in comparison with apply the binomial series to show that
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