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Spring oscillations A spring hangs from the ceiling at equilibrium with a mass attached to its end. Suppose you pull downward on the mass and release it 10 inches below its equilibrium position with an upward push. The distance x (in inches) of the mass from its equilibrium position after t seconds is given by the function x(t) = 10 sin t − 10 cos t, where x is positive when the mass is above the equilibrium position.
- a. Graph and interpret this function.
- b. Find dxdt and interpret the meaning of this derivative.
- c. At what times is the velocity of the mass zero?
- d. The function given here is a model for the motion of an object on a spring. In what ways is this model unrealistic?
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Chapter 3 Solutions
Calculus: Early Transcendentals (2nd Edition)
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