Question

a mass on a spring bounces up and down in simple harmonic motion, modeled by the function

\\s(t) = 3 \cos(t),\\

where \\(s(t)\\) is measured in centimeters and \\(t\\) is measured in seconds. find the rate at which the spring is oscillating at \\(t = 6\\) seconds. round your answer to four decimal places.

Explanation:

Differentiate the position function

$$ v(t) = s'(t) = \frac{d}{dt}[3\cos(t)] = -3\sin(t) $$

Evaluate the velocity at the given time

$$ v(6) = -3\sin(6) $$

Calculate the numerical value

$$ v(6) \approx -3 \times (-0.279415) \approx 0.8382 $$

Answer:

A mass on a spring bounces up and down in simple harmonic motion, modeled by the function \(s(t) = 3\cos(t)\), where \(s(t)\) is measured in centimeters and \(t\) is measured in seconds. Find the rate at which the spring is oscillating at \(t = 6\) seconds. Round your answer to four decimal places.

<blank>0.8382</blank> cm/s