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Wednesday, June 14, 2006

Springy spring


Fused Bulbs
SPRINGY SPRING

Consider the given situation.
The system of spring and the block has maximum potential but minimum kinetic energy

Let U be the potential energy at any instant

At the given situation, potential energy is maximum

: . dU/dx = 0

=> -dU/dx = 0
=> Force = 0

But the force at this position is maximum

Also, d2U/dx2 = k (spring constant) > 0

But the condition for maxima is d2U/dx2 < 0

WHY THIS ANOMALY?

Send your answers to my email address: pravar_isgr8@yahoo.co.in
Don’t post your answers here

4 comments:

Anonymous said...

Force is actually a retarding force that is=-kx to make the force quantiy positive.......or =kx if x is negative so k is -ve so maxima condition stands

Pravar D Mahajan said...

O.K. but what abt du/dx=0? force isn't zero

Arun Chaganty said...

My only explanation is that our function is obivously limited between x = -A, A. So as we all know, differentials are not defined at end points. So this cannot say anything.

basil said...

the U-x graph is not continous at it its end points so we cannot apply the the maxima principle there
try this:the U-t graph is continous every where,so at the maximum potentiel dU/dt=0,1/2kx2/dt=o,kxv=o,v=0,the correct procedure the correct result