Question: Problems 24 through 34 deal with a massspringdashpot system having position function x(t) satisfying Eq. (4). We write x 0 = x(0) and v 0

Problems 24 through 34 deal with a mass–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), w = k/m, and w=w2 - p.

The system is critically damped, overdamped, or underdamped, as specified in each problem.

(Underdamped) Let x1 and x2 be two consecutive local maximum values of x (t). Deduce from the result of Problem 32 that 

The constant Δ = 2πp/ω1 is called the logarithmic decrement of the oscillation. c = mω1Δ/π because p = c/(2m).

p = c/(2m), w = k/m, and w=w2 - p.

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