Homework Assignment 2
Physics 302, Classical Mechanics
Fall 2010
A. V. Kotwal
Handed out:
Friday, Sep. 10, 2010
Due in class on:
Friday, Sep. 17, 2010
Problems
1. A double plane pendulum consists of a simple pendulum (mass
m
1
, length
l
1
) with another simple
pendulum (mass
m
2
, length
l
2
) suspended from
m
1
, both constrained to move in the same vertical
plane.
Write down the Lagrangian of this system in suitable coordinates, and derive Lagrange’s
equations.
2. Consider a stretchable plane pendulum, i.e. a mass
m
suspended from a spring of spring constant
k
and unstretched length
l
, constrained to move in a vertical plane. Write down the Lagrangian and
obtain the EulerLagrange equations.
3. A wire is bent into the shape given by
y
=
A

x
n

, n
≥
2 and oriented vertically, opening upward, in
a uniform gravitational field
g
. The wire rotates at a constant angular velocity
ω
about the
y
axis,
and a bead of mass
m
is free to slide on it without friction. Find the equilibrium height of the bead
on the wire. Consider especially the case
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 Spring '09
 Physics, Mass, Work, Hamiltonian mechanics, Lagrangian mechanics, Euler–Lagrange equation, Plane Pendulum

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