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.

\

$\"\"$ .

\

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 $\"\"$