Solve Spring SHM Problem: Period of Oscillation in M1, M2, k

[brendan3eb]

Homework Statement

Two blocks of mass M2 and M1 (M2>M1) are connected by a spring with force constant k and are free to slide on a frictionless table. They are pulled apart and then released from rest. In terms of M1, M2, and k, what would the period of oscillation be?

Homework Equations

T=2PI*sqrt(m/k)
f=-kx

The Attempt at a Solution

So taking the starting position to be both blocks just before they released, one full cycle would be when they have both returned to their initial positions. Other than noting this, the problem leaves me perplexed as to what to do next..all I need is a hint in the right direction. I guess just picturing such an apparatus in my head is mind-boggling. Would the equilibrium point remain the same or would it start to expand and contract abnormally?

 

[Shooting Star]

The CM wouldn't move, so you could start by taking that as the origin. Take x1 and x2 to be the positions of the masses etc. Now, write the force eqns on the springs. Take x=x1-x2, the dist between the two springs.

Your aim is to only find the w. Once you have reduced the two eqns to a form of Mx'' = -k'x, for some M, then directly you can find w. A bit of algebraic manipulation is reqd.

 

[Moetasim]

As a scientist, your first step should be to identify the variables and parameters in the problem. In this case, the variables are M1, M2, and k and the parameter is the period of oscillation, T.

Next, you should recall the equation for the period of oscillation of a mass-spring system, which is T=2π√(m/k). This equation relates the period of oscillation to the mass and spring constant.

Now, you need to apply this equation to the given problem. Remember that the blocks are connected by the spring, so the total mass in the system is M1+M2. Therefore, the period of oscillation will be T=2π√((M1+M2)/k).

To check if this is the correct solution, you can do a quick sanity check. If M1 is very small compared to M2, the period of oscillation should be close to the period of a single block attached to the spring, which is T=2π√(M2/k). This makes sense because if one block is much smaller, it will have a smaller effect on the period of oscillation.

In terms of the equilibrium point, it will remain the same as the blocks will oscillate around it. As long as the spring remains in the linear region of its force-displacement curve, the blocks will oscillate harmonically. It may help to draw a diagram or create a mental image of the system to better understand the motion.

I hope this helps guide you in the right direction. Remember to always start by identifying the variables and equations that relate them, and then apply them to the given problem. Good luck!