Consider three particles of mass m, M, and m respectively, joined through ideal springs of natural length L0 and elasti
Posted: Mon May 09, 2022 2:29 pm
Consider three particles of mass m, M, and m respectively,
joined through ideal springs of natural length L0 and elastic
constant k as shown in the figure. Particles can be moved
only on the x-axis.
a) Write the Lagrangian of the system.
b) Find the equations of motion of the system.
c) Find the equilibrium positions of the system and define the
deviation variables qi.
d) Suppose qi = A0i exp(iΩt), and show that the problem of finding
the frequencies of this system boils down to a problem of
eigenvalues and vectors.
e) Find the oscillation frequencies (Ω21, Ω2, Ω23).
f) Find the normal solutions or modes (A01, A02, A03) for each
frequency.
M ա ա 200 k k
joined through ideal springs of natural length L0 and elastic
constant k as shown in the figure. Particles can be moved
only on the x-axis.
a) Write the Lagrangian of the system.
b) Find the equations of motion of the system.
c) Find the equilibrium positions of the system and define the
deviation variables qi.
d) Suppose qi = A0i exp(iΩt), and show that the problem of finding
the frequencies of this system boils down to a problem of
eigenvalues and vectors.
e) Find the oscillation frequencies (Ω21, Ω2, Ω23).
f) Find the normal solutions or modes (A01, A02, A03) for each
frequency.
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