Consider a spring subject to a frictional or damping force. (a) In the critically damped case, the motion is given by x = c1e^rt c2 te^rt . Show that the graph of x crosses the t -axis whenever c1 and c2 have opposite signs. (b) In the overdamped case, the motion is given by x = c1e^r1t c2 e^r2t , where r1 > r2 . Determine a condition on the relative magnitudes of c1 and c2 under which the graph of x crosses the t -axis at a positive value of t . | Numerade
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