Question

(1 point) Suppose a pendulum with length L (meters) has angle 0 (radians) from the vertical. It can be shown that 0 as a function of time satisfies the differential equation: d20 + -sin 0 = 0 dt2 L where g = 9.8 m/sec/sec is the acceleration due to gravity. For small values of 0 we can use the approximation sin(0) ~ 0, and with that substitution, the differential equation becomes linear A. Determine the equation of motion of a pendulum with length 1.5 meters and initial angle 0.2 radians and initial angular velocity deldt 0.4 radians/sec B. At what time does the pendulum first reach its maximum angle from vertical? (You may want to use an inverse trig function in your answer) seconds C. What is the maximum angle (in radians) from vertical? D.How long after reaching its maximum angle until the pendulum reaches maximum deflection in the other direction? (Hint: where is the next critical point?) seconds E. What is the period of the pendulum, that is the time for one swing back and forth? seconds

Answer 1

in-0 all anle 8n9 dt thut equhon is in(wt+ Galution 2d ,2 = ,in tW .56a/ses de out at to and n p CoAd tan( 2 W 28 2 J 9.8 4 9rad -2rad in 2 , 25 ) eguahon in(.S6t+.9) ad

(2) E) for madimum ginl.set+) . 56-t .26. 8ec (c) Maximum avgle fom verical is fint 3 Time between two cmtical I: 2 1-23 ce T 2