A spring of force constant `1200Nm^(-1)` is mounted on a horizontal table as shown in figure. A mass of 3.0kg is attached to the free end of the spring, pulled side ways to a distance of 2.0cm and released , what is
(a) the speed of the mass when the spring is compressed by 1.0cm?
Potential energy of the mass when it momentarily comed to rest ?
(c) Total energy of the oscillating mass.

Explanation

`m=3kg,k=1200Nm^(-1)`,
`a=0.92m`
(a) `V+?, y=1.0cm=0.01m. `
Let , `y=asinomegat`
`=aomegasqrt(1-sin^(2)omegat)`
or `V=aomega(1-y^(2)//a^(2))^(1//2)`
`=omegasqrt(a^(2)-y^(2))=sqrt((k)/(m))sqrt((a^(2)-y^(2)))`
`=sqrt((1200)/(3))[(0.02)^(2)-(0.01)^(2)]^(1/(2))`
(b) Max. P.E., `U_(max)-(1)/(2)momega^(2)y^(2)_(max)`
`=(1)/(2)momega^(2)a^(2)=(1)/(2)ka^(2)=(1)/(2)xx1200xx(0.02)^(2)`
`=0.24J`
(c) At the extreme position, where `y=a` the mass just comes to res, its K.E. becomes zero
`:.` Total energy `=P.E. +K.E. =0.24+0`
`=0.24J`