Determine the maximum angular displacement and the rate of change

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.

Comments

the maximum angular displacement is actually 0.2 radians. The 2nd part of your answer is correct.

Answer 1

Step 1:

The function is .

where is angular displacement in radians.

is time in seconds.

.

Apply derivative on each side with respect to .

Use derivative of trigonometric function property:.

Step 2:

The distance of the pendulum is and seconds.

Radius of the pendulum is equal to the half of the distance of the pendulum

.

The maximum angular displacement is .

Substitute in above function.

The maximum angular displacement is radians.

Step 3:

Rate of change of when seconds.

Substitute in above function.

Hence,

Rate of change of is

Solution:

The maximum angular displacement is radians.

Rate of change of is