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The figure below shows a pendulum with length L and the angle 0 from the vertical to the pendulum. It can be shown that 0, as a function of time, satisfies the following nonlinear differential equation 1²0 de2 200 9 + sin0 = 0 where a denotes the acceleration due to gravity. For small values of 0 we can assume 8- sin 8 (g=9.8m/s^2) such that the differential equation can be considered to be linear. Find the equation of motion of the pendulum with length 750 cm if e is initially 15° and its initial angular velocity is de = 1 rad/s. What is the maximum angle from the vertical?

The figure below shows a pendulum with length L and the angle 0 from the vertical to the pendulum. It can be shown that 0, as a function of time, satisfies the following nonlinear differential equation 1²0 de2 200 9 + sin0 = 0 where a denotes the acceleration due to gravity. For small values of 0 we can assume 8- sin 8 (g=9.8m/s^2) such that the differential equation can be considered to be linear. Find the equation of motion of the pendulum with length 750 cm if e is initially 15° and its initial angular velocity is de = 1 rad/s. What is the maximum angle from the vertical?

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(a) D The figure below shows a pendulum with length L and the angle 0 from the vertical to the pendulum. It can be shown that 0, as a function of time, satisfies the following nonlinear differential equation (e) d'o dt2 ( + sin0 = 0 where denotes the acceleration due to gravity. g For small values of 0 we can assume (b) What is the maximum angle from the vertical? 8 sing (g-9.6m/s^2) www. such that the differential equation can be considered to be linear. Find the equation of motion of the pendulum with length 750 cm if e is initially 15° and its initial angular velocity is de = 1 rad/s (d) When will the pendulum be vertical from initial position, that is, 8=0? What is the period of the pendulum (the time to complete one back-and-forth swing)? What is the angular velocity when the pendulum is vertical? Describe how the pendulum concept is used in the pendulum clock. (mar (1) mar
Transcribed Image Text:(a) D The figure below shows a pendulum with length L and the angle 0 from the vertical to the pendulum. It can be shown that 0, as a function of time, satisfies the following nonlinear differential equation (e) d'o dt2 ( + sin0 = 0 where denotes the acceleration due to gravity. g For small values of 0 we can assume (b) What is the maximum angle from the vertical? 8 sing (g-9.6m/s^2) www. such that the differential equation can be considered to be linear. Find the equation of motion of the pendulum with length 750 cm if e is initially 15° and its initial angular velocity is de = 1 rad/s (d) When will the pendulum be vertical from initial position, that is, 8=0? What is the period of the pendulum (the time to complete one back-and-forth swing)? What is the angular velocity when the pendulum is vertical? Describe how the pendulum concept is used in the pendulum clock. (mar (1) mar
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