) Suppose a pendulum with length L (meters) has angle e (radians) from the vertical. It can be shown that 0 as a function of time satisfies the differential equation: d20 sin 0 = 0 L' dt2 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 2 meters and initial angle 0.2 radians and initial angular velocity de/dt 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? nout oritiool point2)

University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter1: Units And Measurement
Section: Chapter Questions
Problem 81AP: Consider the equation s=s0+v0t+a0t2/2+j0t3/6+s0t4/24+ct5/120 , were s is a length and t is a time....
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) 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:
sin 0 = 0
dt?
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 2 meters and initial angle 0.2 radians and initial angular velocity de/dt 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
Transcribed Image Text:) 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: sin 0 = 0 dt? 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 2 meters and initial angle 0.2 radians and initial angular velocity de/dt 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
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