Question

A 15-centimeter pendulum moves according to the equation θ = 0.2 cos 8t, where θ is the angular displacement from the vertical in radians and t is the time in seconds. Determine the maximum angular displacement and the rate of change of θ when t=3 seconds.

Answer 1

To find the maximum angular displacement, find the amplitude of the cosine function. To find the rate of change of θ, take the derivative of the cosine function and evaluate it when t = 3 seconds.

Step-by-step explanation:

To determine the maximum angular displacement, we need to find the amplitude of the cosine function. In the equation θ = 0.2 cos 8t, the coefficient of the cosine function is 0.2. The maximum value of the cosine function is 1, so the maximum angular displacement is 0.2 radians. To find the rate of change of θ when t = 3 seconds, we need to find the derivative of θ with respect to t. The derivative of cos 8t is -8 sin 8t. Substituting t = 3 into this derivative gives us: -8 sin (8 * 3) = -8 sin 24. Evaluating this expression gives us the rate of change of θ when t = 3 seconds.