Question

(radians) from the vertical. It can be shown that as a function of time satisfies the (1 point) Suppose a pendulum with length L (meters) has angle differential equation: d20 + & sin 0 = 0 dt 2 L where g = 9.8 m/sec/sec is the acceleration due to gravity. For small values of we can use the approximation sin() ~ 0, and with that substitution, the differential equation becomes linear. A. Determine the equation of motion of a pendulum with length 1 meters and initial angle 0.1 radians and initial angular velocity deldt 0.1 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

devt i sina so given = im at sikrodias 9=9,8 mlir a) Ser + 915.0 0 do +9160-0 characteristic enation Stais co = I Saigi Olt) = .cicos rairt & Cetinvart Quo) 0) 060).=0.) Olt) = -19.8 c, finaist & Ca Viscos saist 06)=0.) 0,= 4 0 (0) = 0.7 Onl= ca ferig rol 1014) een site to Pinto cos sont t=0 . 8 costart=0 6) olaps sin saist ą R.rcosra.st Jean Fist auf das Itz 0.403 sec The angle i maseemun when t=0.407see

c) 0 (0.403) z o.) Costa 80.403 + 01 Delnas 210-403 = 0.0314 rad is the makering d) the tome leidery ten Tz2x04032 0.8offee e) percod of oscillation 2T so I & Zolsce 1918

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Answer 2

Everything is ok but for D) you have to do 1/2(T), half of the period which is pi/w.

t = pi/w = pi/sqrt9.8