Suppose a pendulum with length L (meters) has angle (radians) from the vertical. It can be shown that as a function of time satisfies the differential equation: d²0 9 + sin 0 = 0 dt2 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) 0, and with that substitution, the differential equation becomes linear. A. Determine the equation of motion of a pendulum with length 0.5 meters and initial angle 0.3 radians and initial angular velocity de/dt 0.3 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?

Suppose a pendulum with length L (meters) has angle (radians) from the vertical. It can be shown that as a function of time satisfies the differential equation: d²0 9 + sin 0 = 0 dt2 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) 0, and with that substitution, the differential equation becomes linear. A. Determine the equation of motion of a pendulum with length 0.5 meters and initial angle 0.3 radians and initial angular velocity de/dt 0.3 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?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.3: Euler's Method

Problem 15E: Use Eulers method to approximate the indicated function value to 3 decimal places, using h=0.1....

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