Write equation of a trigonometric function modeling height

Reference no: EM13984690

A large spring fixed to a board oscillates up and down. When friction is ignored, its height above its midline is modeled by a purely sinusoidal function S(t) feet, t seconds after its movement is initiated.

a. The spring begins at its lowest value of 8 inches below its midline, and, without friction, returns 5 times per second to this lowest value. Write the equation of a trigonometric function modeling the height above its midline.

b. When friction is accounted for. the spring's height is instead modeled by H(t) = D(t) S(t), where D(t) is a so-called "damping" function of the form D(t) = e^-kt for some positive constant k. Using the constant k, write the equation for H(t). If your answer involves kt. somewhere, write k * t. otherwise. WeBWork may not be able to separate them.

c. Given that after 0.666667 seconds of damped motion (motion with friction) the spring is at a height of 3 inches above its midline, find the value of k.

d. Compute the value of if H(2.6).

Reference no: EM13984690

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