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    DE spring problem

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    DE: 32 pound weight is attached to the lower end of a coiled spring suspended from the ceiling, spring constant being 3 pounds per foot. The weight is pushed upward by 5 feet and given downward velocity of 3 feet per second. The medium it is in offers a resistance in pounds numerically equal to 4 times the instantaneous velocity in feet per second.

    1) determine the times when the weight will pass through equilibrium.

    Note: I already found the equation of motion to be x(t)= -6e^(-t) + e^(-3t).

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    https://brainmass.com/math/partial-differential-equations/de-spring-problem-434733

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