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.

Deduce from Problem 24 that x(t) has a local maximum or minimum at some instant t > 0 if and only if v0 and v0 + px0 have the same sign.

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

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To deduce that xt has a local maximum or minimum at some instant t 0 if and only if v0 and v0 px0 have the same sign we can analyze the behavior of the solution to the given secondorder linear homogen... View full answer

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