Question

Suppose some particle of mass m is confined to move, without
friction, in a vertical plane, with axes x horizontal and y
vertically up. The plane is forced to rotate with angular velocity
of magnitude Ω about the y axis. Find the equation of motion for x
and y, solve them, and describe the possible motions. This is not
meant to be a lagrangian problem.

Answer #1

a particle of mass m is constrained to move under gravity
without friction in side of paraboloid of revolution whose axis is
vertical. find the one dimentional problem equivalent to its
motion. what is the condition on particle;s initial velsity to
produce circular motion? find the period of small oscilations about
this circular motion.

URGENT (need within 1.5 hour)
A particle of mass M is confined to move in the x-y plane, and
is subjected to the following potential
V(x,y) = 1⁄2 k1 x2 + 1⁄2 k2 y2
where k1 and k2 are the spring constants restricting the motion,
and k1 << k2.
(a) Write down the Schrodinger equation for the particle, and
show the steps to solve the equation, assuming the solution of the
one-dimensional Harmonic oscillator is known.
(b) Write down the...

Goldstein Classical Mechanics, 3rd Edition. Chapter 6; exercise
3 Question: A bead of mass m is constrained to move on a hoop of
radius R.The hoop rotates with constant angular velocity small
omega around a diameter of the hoop,which is a vertical axis (line
along which gravity acts). (a) set up the Lagrangian and obtain the
equations of motion of the bead. (b) Find the critical angular
velocity large/capital omega below which the bottom of the hoop
provides a stable...

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