Find position of two masses at any time

[leonne]

Homework Statement

2 particles are joined by mass less spring of length L. m2 initially resting on table and i am holding m1 vertically above m2 at height L. I project m1 vertically upwards with initial velocity Vo
find position of the two masses at any time and describe motion

Homework Equations

L=t-u

The Attempt at a Solution

I just need help finding the kinetic and potential of the system.
ok so in this system we have 2 potentials right? One is gravity and the other is the spring?
For the kinetic, we use the center of mass?

they get L= 1/2(M$$\stackrel{.}{Y}$$²-MgY+ 1/2($$\mu$$$$\stackrel{.}{y}$$²-1/2(k(y-L)²)

for kinetic we use the center of mass formula right t=1/2MR² +1/2($$\mu$$r²

Why exactly do they have Y than y is Y for mass 1 and y for mass 2? If so than the two potentials, one of them acts on one block and the other one on the other block?

o also how do we know when to use the center of mass formula? there was another problem with pendulum in a moving elevator and didn't use the center of mass formula

ok and to find position of the two masses, after solving the Lagrangian you are given equation of motion and i would think just take the derivative but that's not posible from the answer they get
Thanks

 

[NateD]

Yes you are right, Y is for mass 1 and y is for mass 2. The two potentials act on the two blocks separately, one is the gravitational potential (acting on both) and the other is the potential of the spring (acting only on the second block).For the center of mass formula, it is used when you have a system with more than one particle, in this case two particles. The elevator problem is a single particle system so the center of mass formula does not apply.To find the position of the two masses, after solving the Lagrangian you will be given equations of motion for each particle. To find the positions of the two masses at any time, you just need to integrate these equations.