Suppose a pendulum of length $L$ meters makes an angle of $\theta$ radians with the vertical, as in the figure. It can be shown that as a function of time, $\theta$ satisfies the differential equation $$\frac{d^2\theta}{dt^2} + \frac{g}{L} \sin\theta = 0,$$ where $g = 9.8 \ \mathrm{m/s^2}$ is the acceleration due to gravity. For $\theta$ near zero we can use the linear approximation $\sin(\theta) \approx \theta$ to get a linear differential equation $$\frac{d^2\theta}{dt^2} + \frac{g}{L} \theta = 0.$$ Use the linear differential equation to answer the following questions. (a) Determine the equation of motion for a pendulum of length $0.5$ meters having initial angle $0.3$ radians and initial angular velocity $\displaystyle \frac{d\theta}{dt} = 0.1$ radians per second. $\theta(t) =$ radians (b) What is the period of the pendulum? That is, what is the time for one swing back and forth? Period = seconds

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