A pendulum consists of a mass m and a massless stick of length l. The pendulum support oscillates horizontally with a position given by x = A cos (wt), as shown below. Use 0 (the angle of the pendulum as measured from the vertical) as your generalized coordinate. In HW 8, you found the Lagrangian of this system is: 1 L = ·m (1² j² + x² + 2lxė cos 0 ) + mgl cos 0 m Use the Euler-Lagrange equation to find the equation of motion for this system. Then make a small angle approximation cos 0 ~ 1. The equation you find should be recognizable as the equation for a driven oscillator. What is the solution for 0 (t) in the small angle approximation?
A pendulum consists of a mass m and a massless stick of length l. The pendulum support oscillates horizontally with a position given by x = A cos (wt), as shown below. Use 0 (the angle of the pendulum as measured from the vertical) as your generalized coordinate. In HW 8, you found the Lagrangian of this system is: 1 L = ·m (1² j² + x² + 2lxė cos 0 ) + mgl cos 0 m Use the Euler-Lagrange equation to find the equation of motion for this system. Then make a small angle approximation cos 0 ~ 1. The equation you find should be recognizable as the equation for a driven oscillator. What is the solution for 0 (t) in the small angle approximation?
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![A pendulum consists of a mass m and a massless stick of length l. The pendulum support oscillates
horizontally with a position given by x = A cos (wt), as shown below. Use 0 (the angle of the
pendulum as measured from the vertical) as your generalized coordinate. In HW 8, you found the
Lagrangian of this system is:
1
L = ·m
(1² j² + x² + 2lxė cos 0 ) + mgl cos 0
m
Use the Euler-Lagrange equation to find the equation of motion for this system. Then make a
small angle approximation cos 0 ~ 1. The equation you find should be recognizable as the equation
for a driven oscillator. What is the solution for 0 (t) in the small angle approximation?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4366330b-8089-40e4-b3cc-07cdde1ff8ae%2Fdc202797-0dc6-4c11-8257-b0457a6ebfb6%2Fc11yh7g_processed.png&w=3840&q=75)
Transcribed Image Text:A pendulum consists of a mass m and a massless stick of length l. The pendulum support oscillates
horizontally with a position given by x = A cos (wt), as shown below. Use 0 (the angle of the
pendulum as measured from the vertical) as your generalized coordinate. In HW 8, you found the
Lagrangian of this system is:
1
L = ·m
(1² j² + x² + 2lxė cos 0 ) + mgl cos 0
m
Use the Euler-Lagrange equation to find the equation of motion for this system. Then make a
small angle approximation cos 0 ~ 1. The equation you find should be recognizable as the equation
for a driven oscillator. What is the solution for 0 (t) in the small angle approximation?
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