Lagrangian Mechanics: A pendulum of mass m and length l hangs from the rear view mirror...
Lagrangian Mechanics:
A pendulum of mass m and length l hangs from the rear view mirror in a car traveling with horizontal acceleration a. Assume the car starts from rest at time t=0. (Solve using Lagrangian Mechanics.)
a) Draw a diagram of the situation. Write out the x and y coordinates of the position of the pendulum in the in terms of the angle of the pendulum, Φ, and the time t.
b) Write out T, U, and L in terms of the angle of the pendulum, Φ, and the time t.
c) Solve the E-L equation for the equation of motion for the pendulum bob. Find the equilibrium angle for the pendulum and show that it is equal to: Φo = tan-1(a/g)
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Lagrangian Mechanics:
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