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`        two blocks of masses m and m' are connectd by a light spring on a horizantal frictionless table.the spring is compressed and then released.Find the ratio of accelaration and masses`
7 years ago

SAGAR SINGH - IIT DELHI
879 Points
```										Dear apraitm,
Let k be the spring constant of the spring.
Here reduced mass concept will be applicable. so reduced mass of the system is M= mm'/(m+m')
or this solution, I will already assume that all motion takes place in the x-direction.  So, I can write Newton's second law as:

Where Fx is the total force (there is only one in this  case anyway).  Please forgive me, but I am going to drop the "in the  x-direction" notation since EVERYTHING is only in the x-direction.  The  force from the spring is:

Remember that this spring has zero natural length, so the x position IS the "stretch".  Putting this together, I get:

Here I wrote acceleration as the second time derivative of position.   If that is something completely foreign to you, don't worry - you will  see this later maybe.  Anyway, what I have here is a differential  equation.  How do you solve a differential equation?  There are lots of  strategies, but I find the best one is to guess.  Yes, just guess a  solution and see if it works.  First, let me re-write the differential  equation:

If you look at this equation, it says "take the derivative with  respect to time twice and get something times the original function"  (really, it says that, you might have to listen closely).  Once function  that does that is ....cosine.  So, let me try the function:

Where A and ? are constants.  Let me take the first derivative:

And now the second derivative:

So this means that:

ACCELERATION=Kx(m+m')/(mm')

We are all  IITians and here to help you in your IIT  JEE preparation.  All the best.

Sagar Singh
B.Tech IIT Delhi
sagarsingh24.iitd@gmail.com

```
7 years ago
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