(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A uniform disk of mass M and radius a can roll along a rough horizontal rail. A particle of mass m is suspended from the center C of the disk by a light inextensible string b. The whole system moves in a vertical plane through a rail. Take as generalized coordinates x, the horizontal displacement of C, and theta , the angle between the string and the downward vertical. Obtain Lagrange's equation . Show that x is a cyclic coordinate and find the corresponding conserved momentum p_x. Is p_x the horizontal linear momentum of the system?

Given that theta remains small in the motion , find the period of the small oscillations particle.

2. Relevant equations

Ihave to “linearize” the θ equation, after eliminating derivitives

of x, to get an equation for θ that is eﬀectively simple harmonic motion.

In this case, linearizing means assuming θ and ˙

θ are small, approximat-

ing all of the trigonometric functions up to terms linear in θ, and throwing

out terms quadratic in θ and ˙

θ. Soln.: the period for small oscillations is

q

3M b

.

3. The attempt at a solution

x_1=q_1-F y_1=0 z_1=0

x_2=q_1+a*sin(q_2)-F,y_2=0,z_1=-a*cos(q_2)

Not sure what to do after that

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# Homework Help: Lagrange equation problem involving disk

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