The height, h , in feet of a ball suspended from a spring as a function of time, t , in seconds can be modeled by the equation h is equal to A sine open paren b times open paren t minus h close paren close paren plus k What is the height of the ball at its equilibrium?

In a sinusoidal model of the form A sin(b(t − something)) + k, the value k is the midline, or equilibrium height. The amplitude A describes how far the ball moves above and below that height, so the ball’s equilibrium height is k feet.

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