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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?
(b) Potential energy of the mass when it momentarily comes to rest ?
(c) Total energy of the oscillating mass.
image

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Here, `k=1200Nm^(-1),m=3.0kg,`
`y=1.0cm =0.01m,`
`a=2.0cm=0.02m`
(a) Speed, `V=omegasqrt(a^(2)-y^(2))`
`=sqrt((k)/(m))(a^(2)-y^(2))^(1//2)`
`sqrt((1200)/(3))[(0.02)^(2)-(0.01)^(2)]^(1//2)`
`=0.346ms^(-1)`
(b) The body is momentarily at rest, when `y=a`
`P.E. =(1)/(2)ka^(2)=(1)/(2)xx1200xx(0.02)^(2)=0.24J`
(c) Total energy `=` P.E. `+` K.E.
`=0.24+0=0.24J`

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