A mass on a spring bounces up and down in simple harmonic motion, modeled by the function \( s(t)=3 \cos t \) where \( s \) is measured in centimeters and \( t \) is measured in seconds. Find the rate at which the spring is oscillating at \( t=8 \mathrm{~s} \). Round your answer to four decimal places.

To find the rate at which the spring is oscillating at \( t=8 \) seconds, we need to find the derivative of the function \( s(t) = 3 \cos t \) with respect to time \( t \) and then evaluate it at \( t=8 \) seconds. Given function: \( s(t) = 3 \cos t \) 1. Find the derivative of \( s(t) \) with respect to \( t \): \[ s'(t) = \frac{d}{dt} (3 \cos t) \] 2. Calculate the derivative: \[ s'(t) = -3 \sin t \] 3. Evaluate the derivative at \( t=8 \) seconds: \[ s'(8) = -3 \sin(8) \] 4. Calculate the value of \( s'(8) \) and round it to four decimal places. Let's calculate the value of \( s'(8) \) and round it to four decimal places. Calculate the value by following steps: - step0: Calculate: \(-3\sin\left(8\right)\) The rate at which the spring is oscillating at \( t=8 \) seconds is approximately -2.9681 cm/s.