Mathematics

Problem

The angular displacement (in radians) of a pendulum from its resting position is modeled by

\theta(t)=0.3\,\sec\!\bigl(0.2t-\dfrac{\pi}{6}\bigr)

for

0\le t\le10

, where

t

is measured in seconds. (a) Derive an expression for the angular velocity

\dfrac{d\theta}{dt}

as a function of

t

. (b) Compute the angular velocity at

t=2.5

seconds. Give an exact value. (c) Determine all values of

t

in the interval

0<t<10

for which the magnitude of the angular velocity equals 1 rad/s. Show all work leading to your answer. (d) Interpret the physical meaning of your result from part (c) in the context of the pendulum's motion.

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