Two blocks of masses `m_(1)` and `m_(2)` interconnect with a spring of stiffness `K`, are kept on as smooth horizontal surface. Find out the ratio of velocity, displacement, kinetic energy and acceleration block with mass `m_(1)` of block with mass `m_(2)`.

Explanation

Here `x` is the displacement, `v` is the speed, `p` is the mometum, a is the accelertion, `KE` is the kinetic energy, `F` is the force
`(F_(ext))_("system")=0impliesvecp_(1)+vecp_(2)=0`
`m_(1)v_(1)=m_(2)v_(2)impliesv_(1)/v_(2)=m_(2)/m_(1)`
`m_(1)int_(0)^(1)v_(1)dt=m_(2)int_(0)^(1)v_(2)dt`
where `t` is the time interval of motion of each block.
`m_(1)x_(1)=m_(2)x_(2)impliesx_(1)/x_(2)=m_(2)/m_(1)`
`(KE_(1))/(KE_(2))=(P_(1)^(2)//2m_(1))/(P_(1)^(2)//2m_(2))=m_(2)/m_(1)` (`:'p_(1)=p_(2))`
`impliesF_(1)/F_(2)=(kx)/(kx)`
where `x` is the deformation of the spring.
`:. F_(1)/F_(2)=1=(m_(1)a_(1))/(m_(2)a_(2))=1impliesa_(1)/a_(2)=m_(2)/m_(1)`