- #1

Aziza

- 190

- 1

## Homework Statement

Two masses are connected by spring and slide freely without friction along horizontal track. What is period of oscillation?

## Homework Equations

## The Attempt at a Solution

My solution:

let x1 be position of mass 1 (m1) and x2 be position of mass 2 (m2) and L be length of spring in equilibrium.

Then, the total stretch of the spring is x2-x1-L. Also, F1 = -F2. Thus:

m1(x1)'' = -k(x1 - x2 + L)

m2(x2)'' = -k(x2 - x1 - L)

Solving for x2 from first eqn and substituting back into second eqn yield:

[itex]\frac{d^2}{dt^2}[\frac{m1 m2}{k}(x1)''+(m1+m2)x1][/itex] = 0

I am unsure how to proceed from here, any hints? I would like to just multiply both sides by (dt^2)/d^2 but I am unsure if this is mathematically correct? It does simplify the problem though and gives me right answer...

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