A block of mass m, attached to a spring of spring constant k, oscilltes on a smooth horizontal table. The other end of the spring is fixed to a wall. If it has speed v when the spring is at its naturla lenth, how far will it move on the table before coming to an instantaneous rest?

Options

A. `x=sqrt((m)/(kupsilon))`
B. `x=(1)/(upsilon)sqrt((m)/(k))`
C. `x=upsilonsqrt((m)/(k))`
D. `x=sqrt((muupsilon)/(k))`

Answer

C

Explanation

Time period, `T=2pisqrt((m)/(k))` and `omega=(2pi)/(T)=sqrt((k)/(m)),`
When the spring is at its natural length, the velocity of block is maximum. So `upsilon=romega`. In question
`r=x, `so `upsilon=xomega` or `x=(upsilon)/(omega)=upsilonsqrt((m)/(k))`