IIT JEE , AIEEE Forum - Physics , Mechanics

elastiboysai

Consider 2 blocs m1 and m2 attached to each other by a massless spring
of force constant k.
Supposer l is the free length of spring,
consider ur system 2 b placed on x axis, with 1 mass m2 at origin.
if m1 and m2 are displaced and have coordinates by x1 and x2
extension of spring= x =(x1-x2)-l --->1
now
m₁d²x₁/dt² =-kx
m₂d²x₂/dt² =kx
from the abov 2,

m₁m₂d²(x₁-x₂)/dt²=-kx(m₁+m₂)
m₁m_2/(m₁+m₂)--=y say
differentiating 1 twice we get
yd²x/dt²=-kx
so
d²x/dt²= -k/y *x
here y plays the role of mass.
We can straightaway use d standard equations by treating y as the mass.

I agree my proof is not rigorous.
Reduced mass is just a technique .
If no external force acts on the system and only internal conservative forces are in play,
mechanical energy of the system will remain conserved.
in such cases , u cn play wid reduced mass

The abov problem is such an example
To the system of 2 masses, gravitational force between them is an internal conservative froce n u can use d same technique..

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