Two-Mass Spring System: Find Position of Second Mass as a Function of Time

[upurg]

I have a system like this:

Wall-spring-mass-spring-mass

Both springs follow Hooks law with spring-constant k.
The masses are both m.

At rest, the first mass is at x=1 and the second at x=2

At t=0 the springs are pulled so that the first mass is at x=2 and the second at x=7.

Find the position of the second mass as a function of t.

 

[Meir Achuz]

You have to use normal modes. Look that up in your textbook.

 

[K^2]

If you are having difficulty, your first step is to write the equations of motion for x₁ and x₂ to be of the form

$$\ddot{x} = Kx$$

where x is a vector containing x₁ and x₂ and K is a constant 2x2 matrix. If you don't know what to do from there, do what Meir Achuz suggested. A typical ODE book would also have explanation on how to solve such a system of equations.