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3. Consider a pendulum with mass m at the end of massless rigid rod of length l, with the pivot attached to another mass M which is free to slide without friction along a straight horizontal rail. Take the generalized coordinates to be the position x of the pivot, and the angle 0 that the pendulum makes with the vertical direction. (a) Write down the Lagrangian and derive the equations of motion. (b) Find the frequency of small oscillations around the stable equilibrium. (c) Now suppose a force acts on the the mass M causing it to travel with constant acceleration a in the positive x direction. Find the equilibrium angle 0 of the pendulum.

3. Consider a pendulum with mass m at the end of massless rigid rod of length l, with the pivot attached to another mass M which is free to slide without friction along a straight horizontal rail. Take the generalized coordinates to be the position x of the pivot, and the angle 0 that the pendulum makes with the vertical direction. (a) Write down the Lagrangian and derive the equations of motion. (b) Find the frequency of small oscillations around the stable equilibrium. (c) Now suppose a force acts on the the mass M causing it to travel with constant acceleration a in the positive x direction. Find the equilibrium angle 0 of the pendulum.

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a, b, and c please 3. Consider a pendulum with mass m at the end of massless rigid rod of length l, with the pivot attached to another mass M which is free to slide without friction along a straight horizontal rail. Take the generalized coordinates to be the position x of the pivot, and the angle 0 that the pendulum makes with the vertical direction. (a) Write down the Lagrangian and derive the equations of motion. (b) Find the frequency of small oscillations around the stable equilibrium. (c) Now suppose a force acts on the the mass M causing it to travel with constant acceleration a in the positive r direction. Find the equilibrium angle 0 of the pendulum.
Transcribed Image Text:a, b, and c please 3. Consider a pendulum with mass m at the end of massless rigid rod of length l, with the pivot attached to another mass M which is free to slide without friction along a straight horizontal rail. Take the generalized coordinates to be the position x of the pivot, and the angle 0 that the pendulum makes with the vertical direction. (a) Write down the Lagrangian and derive the equations of motion. (b) Find the frequency of small oscillations around the stable equilibrium. (c) Now suppose a force acts on the the mass M causing it to travel with constant acceleration a in the positive r direction. Find the equilibrium angle 0 of the pendulum.
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