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Suppose a pendulum of length L meters makes an angle of 0 radians with the vertical, as in the figure. It can be shown that as a function of time, e satisfies the differential equation d²0e de+sin 8- 0, where g 9.81 m/s² is the acceleration due to gravity. For near zero (small) we can use the linear approximation sin() to get a linear differential equation dt2 Answer the following questions. The pendulum of length 0.5 meters have initial angle 0.5 radians and initial angular velocity de 0.2 radians per second. (a) What is the amplitude of the pendulum? 8- radians (b)Determine the equation of motion for the pendulum e(t)-radians (b) What is the period of the pendulum? That is, what is the time for one swing back and forth? Period= seconds 0 L

Suppose a pendulum of length L meters makes an angle of 0 radians with the vertical, as in the figure. It can be shown that as a function of time, e satisfies the differential equation d²0e de+sin 8- 0, where g 9.81 m/s² is the acceleration due to gravity. For near zero (small) we can use the linear approximation sin() to get a linear differential equation dt2 Answer the following questions. The pendulum of length 0.5 meters have initial angle 0.5 radians and initial angular velocity de 0.2 radians per second. (a) What is the amplitude of the pendulum? 8- radians (b)Determine the equation of motion for the pendulum e(t)-radians (b) What is the period of the pendulum? That is, what is the time for one swing back and forth? Period= seconds 0 L

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Suppose a pendulum of length L meters makes an angle of @ radians with the vertical, as in the figure. It can be shown that as a function of time, e satisfies the differential equation +sin 8-0, where g 9.81 m/s² is the acceleration due to gravity. For near zero (small) we can use the linear approximation sin() to get a linear differential equation d'e dt2 +/-0. Answer the following questions. The pendulum of length 0.5 meters have initial angle 0.5 radians and initial angular velocity 0.2 radians per second. de (a) What is the amplitude of the pendulum? 8-radians (b)Determine the equation of motion for the pendulum 8(t)=radians (b) What is the period of the pendulum? That is, what is the time for one swing back and forth? Period= seconds L
Transcribed Image Text:Suppose a pendulum of length L meters makes an angle of @ radians with the vertical, as in the figure. It can be shown that as a function of time, e satisfies the differential equation +sin 8-0, where g 9.81 m/s² is the acceleration due to gravity. For near zero (small) we can use the linear approximation sin() to get a linear differential equation d'e dt2 +/-0. Answer the following questions. The pendulum of length 0.5 meters have initial angle 0.5 radians and initial angular velocity 0.2 radians per second. de (a) What is the amplitude of the pendulum? 8-radians (b)Determine the equation of motion for the pendulum 8(t)=radians (b) What is the period of the pendulum? That is, what is the time for one swing back and forth? Period= seconds L
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