Suppose a pendulum of length L meters makes an angle of 8 radians with the vertical, as in the figure. It can be shown that as a function of time, @ satisfies the differential equation &0 g . W+fSln0:O, where g = 9.8 m/ s? is the acceleration due to gravity. For # near zero we can use the linear approximation sin(6) =~ 6 to get a linear differential equation a9 g A Use the linear differential equation to answer the following questions. (a) Determine the equation of motion for a pendulum of length 2 meters having initial angle 0.3 radians and initial angular d velocity i = (.5 radians per second. a(t) = | radians L ) (b) What is the period of the pendulum? That is, what is the time for one swing back and forth? Period = | 2.84 seconds