- #1
CGandC
- 326
- 34
Homework Statement
A.[/B] Suppose I have a block of mass 'M' that is attached to a wall via spring of coefficient 'k' , the spring has rest length Xo .
Suppose I look at the problem at some time 't' such that the spring is being compressed and the block moves left ( moving towards x = 0 ) , in this case , the diagram will look :
Now , if at this time I apply Newton's second law on the block, I'll get:
m*d2x/dt2 = k*(x-Xo)
Which is wrong ( why? )
I know that I'm supposed to get:
m*d2x/dt2 = -k*(x-Xo)
but I only get this result if I look at the problem at some time 't' such that the body is after Xo and is being
stretched . But this is not the time interval I want.
* So suppose I want to reach the correct equation from the situation when the spring compresses ( the
situation where I got the first equation ) , I know there's wrong with first equation , but why? , after all , the force from Hooke's law does point to the right when the spring compresses , and I know that I shouldn't mingle around with the sign of the acceleration.
B. Suppose I have the same block from question A , but now , I change my coordinates so that the y stays the same and the positive x-axis points to the left, and suppose I look at the block at time 't' such that the block is being stretched after rest length Xo :
So , using Newton's second law on the block , I'll get:
m*d2x/dt2 = k*(x-Xo)
* which is wrong, but why? , after all , since the displacement ' x-Xo ' is negative and by hooke's law:
-k*(x-X0) > 0 so the force is indeed pointing positively in this coordinates.
Homework Equations
F = ma
m*d2x/dt2 = -k*(x-Xo)
The Attempt at a Solution
-