Suppose a pendulum of length L meters makes an angle of 0 radians with the vertical, as in the figure. It can be shown that as a function of time, 0 satisfies the differential equation sin 0 = 0, + dt2 where g = 9.8 m/s² is the acceleration due to gravity. For 0 near zero we can use the linear approximation sin(0) × 0 to get a linear differential equation d²0 0 = 0. dt? Use the linear differential equation to answer the following questions. (a) Determine the equation of motion for a pendulum of length 1.5 meters having initial angle 0.4 radians and initial angular do = 0.1 radians per second. dt velocity 0(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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.