Stuck on this Differential Equations problem. Correct answer will get rated 5 st

Question

Stuck on this Differential Equations problem.

Correct answer will get rated 5 stars.

The figure on page 1179 of your text shows a pendulum with length L(meters) and angle theta (radians) from the vertical to the pendulum. It can be shown that theta as a function of time satisfies the differential equation: where g = 9.8 m/sec/sec is the acceleration due to gravity. For small values of theta we can use the approximation sin(theta) ~ theta, and with that substitution, the differential equation becomes linear. Determine the equation of motion of a pendulum with length 0.5 meters and initial angle 0.4 radians and initial angular velocity d theta/dt 0.3 radians/sec. At what times does the pendulum first reach its maximum angle from vertical? (you may want to use an inverse trig function in your answer) How long after reaching its maximum angle until the pendulum reaches maximum deflection in the other direction? (Hint: where is the next critical point?) What is the period of the pendulum that is the time for one swing back and forth?

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d

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