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Determine the maximum angular displacement and the rate of change

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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.
asked Jan 22, 2015 in CALCULUS by anonymous
the maximum angular displacement is actually 0.2 radians. The 2nd part of your answer is correct.

1 Answer

0 votes

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:.

image

Step 2:

The distance of the pendulum is image and image seconds.

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

image.

The maximum angular displacement is image.

image

Substitute image in above function.

image

The maximum angular displacement is image radians.

Step 3:

Rate of change of when image seconds.

image

Substitute image in above function.

image

Hence, image

Rate of change of is image

Solution:

The maximum angular displacement is image radians.

Rate of change of is image

answered Jan 22, 2015 by james Pupil
edited Jan 22, 2015 by james

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