Suppose a pendulum of length meters
makes an angle of radians with the
vertical, as in the figure. It can be shown that
as a function of time, satisfies the
differential equation
where is the acceleration
due to gravity. For near zero we can
use the linear approximation
to get a linear differential equation
Use the linear differential equation to answer the
following questions.

(a) Determine the equation of motion for a pendulum of
length meters having initial angle
radians and initial angular velocity
radians
per second.

radians

(b) What is the period of the pendulum? That is, what is
the time for one swing back and forth?