A mass is suspended from a spring. When compressed and released, the displacemen

Question

A mass is suspended from a spring. When compressed and released, the displacement of the mass, D(t), is modeled by the function D(t)=2cos 6 pi t (Use exact values, no decimals) a) Find the amplitude, period, and the frequency of this function. Amplitude: ___ Period: ____ Frequency: ____ b) State the coordinates of the "starting point" and of the 'ending point" of the primary cycle of this function. Write the coordinates in ordered pair form. Starting point: ____ Ending point: _____ c) Graph and label the primary cycle for this function. Clearly mark the primary cycle. Label the starting point, halfway point, and the ending point of the primary cycle with their corresponding ordered pair coordinates. Use the scale given in the grid below.

Explanation / Answer

given d(t) = 2 cos(6*pie)t

where amplitude = 2;

frequency f = w/2*pie = 6*pie / 2*pie = 3;

Period = T = 1/f = 1/3 = 0.3333

At t=0, D(0) = 2; starting point is (0,2) and ending point is (0.25,0)

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