Question

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?

Answer 1

Consider the block + the sring as the system. The exterN/Al forces acting on the system are a. the force of gravilty, b. the normal force by the table and c. te force by the wall. None of thes edo any work on this system and hence the total mechanical energy is conserved. If the block mocves a distance x before comming to rest, we have
`1/2 mv^2=1/2kx^2`
or, `x=vsqrt(m/k)`