1. Consider the system on the right; the pendulum (with mass m and length L) is connected to a freely moving block (with mass m). Assume that the surface where the block slides horizontally has negligible friction and the block is connected to a wall by a spring with spring constant k. Determine the (a) frequencies of the normal modes for small oscillations around the equilibrium positions and (b) the motion for each of the normal m L m k modes for special case where w. = Use m Lagrangian formulations to solve the problem.
1. Consider the system on the right; the pendulum (with mass m and length L) is connected to a freely moving block (with mass m). Assume that the surface where the block slides horizontally has negligible friction and the block is connected to a wall by a spring with spring constant k. Determine the (a) frequencies of the normal modes for small oscillations around the equilibrium positions and (b) the motion for each of the normal m L m k modes for special case where w. = Use m Lagrangian formulations to solve the problem.
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Transcribed Image Text:1. Consider the system on the right; the pendulum (with
mass m and length L) is connected to a freely moving
block (with mass m). Assume that the surface where
the block slides horizontally has negligible friction and
the block is connected to a wall by a spring with spring
constant k. Determine the (a) frequencies of the normal
modes for small oscillations around the equilibrium
positions and (b) the motion for each of the normal
m
m
modes for special case where wo =
Use
m
Lagrangian formulations to solve the problem.
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