When does kinetic energy = energy of the object at position x?

1/2 mv^2 = 1/2 kx^2 ?





When does that ever happen for an object attached to a spring. Here ';x'; is denoted as the distance the object travelled from ';x_0'; - the distance that the spring releases itself but does no work (potential energy)?When does kinetic energy = energy of the object at position x?
There are two equations that you need





1) 1/2 mv^2 = 1/2 kx^2





which is the one you provide and





2) 1/2 mv^2 + 1/2 kx^2 = 1/2 mvo^2





which is the total energy of the object (constant) where vo is the initial velocity of the object right before it touches the spring. 1) and 2) are then two equations with two unknowns so go ahead and solve for v and x. I would suggest you solve for v^2 and x^2 first, that would make it easier to simplify.