SHM

by reduced mass system formula
wew have
ω=√3k2m
x_max can be found using two equations
momentum conservation
4v=3v'
v'=4v/3
and
energy conservation
kx_max²=2mv'²
now
x=x_maxsinωt

but akari..

why in the equation u get x_max why not x_min ??

As I see it using that eqn #2 .. will (should, may) give x_min

asish ,

let m move to the right by x₁, and 2m by x₂ to the right

ten distance between m and 2m is( L+ x₂ - x₁)

using momentum conservation and conservation of KE , as akari has done , we can find

x₁ - x₂ = ± (2mv²/3k)^1/2

x₁ - x₂ will be negative when x₁ is to the left , i.e negative of wat we assumed earlier ,
and hence it will account for the condition of max distance

dus distance _max = L + (2mv²/3k)^1/2

distance_min = L - (2mv²/3k)^1/2

and w ecan find eqn by the method wich akari gave

v is initial velocity, v' is velocity at the reqd condition

akari, can u plz explain the reduced mass concept?