Suppose a pendulum of length L meters makes an angle of radians with the vertical, as inthe figure. It can be shown that as a function of time, 0 satisfies the differential equationd²0+d1² Lwhere g = 9.8 m/s2 is the acceleration due to gravity. For near zero we can use the linearapproximation sin(0) 0 to get a linear differential equationd²0 8d1² LUse the linear differential equation to answer the following questions.8(t) =sin 0 = 0,(a) Determine the equation of motion for a pendulum of length 2.5 meters having initial anglede0.3 radians and initial angular velocity = 0.5 radians per second.dtPeriod=+ -0 =0.(b) What is the period of the pendulum? That is, what is the time for one swing back andforth?secondsradians.

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Answered: (a) Determine the equation of motion…

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(a) Determine the equation of motion for a pendulum of length 2.5 meters having initial angle d0 0.3 radians and initial angular velocity 0.5 radians per second. dt 8(t) = (b) What is the period of the pendulum? That is, what is the time for one swing back and forth? Period= radians seconds