Question

A spring bounces up and down according to the model d(t) = 6cos(60t) - 2, where d(t) is the displacement in cm from the rest position and t is time in seconds. What is the range?

Answer 1

The range of the spring's displacement described by the function d(t) = 6cos(60t) - 2 is from -8 cm to 4 cm.

Step-by-step explanation:

The range of the function describing the displacement of a spring in simple harmonic motion, specifically using the model d(t) = 6cos(60t) - 2, can be found by looking at the amplitude and vertical shift of the cosine wave. The amplitude of the wave is 6 cm (from the coefficient in front of the cosine function), and the vertical shift is -2 cm. The maximum displacement occurs when the cosine function is at its peak (equal to 1), resulting in a maximum d(t) of 6 * 1 - 2 = 4 cm. The minimum displacement occurs when the cosine function is at its lowest (equal to -1), resulting in a minimum d(t) of 6 * (-1) - 2 = -8 cm. Thus, the range of the spring's displacement is from -8 cm to 4 cm.