A0.63kg mass rests on top of a vertical spring with spring constant 65n/m. when the mass sits at rest, determine the distance that the spring is compressed from it's equilibrium position.

The mass will sag lower and lower and compress the spring, until the
upward force of the spring is equal to the weight of the mass.  When
that happens, the two forces on the mass (gravity and spring) will be
balanced, and the mass will stop sinking.

-- The weight of the mass is (mass) x (gravity) = (0.63) x (9.8) Newtons.

-- The distance that the spring is compressed is  1 meter / 65 newtons.

(1 meter/65 newtons) x (0.63 x 9.8) newtons = 0.095 meter = 9.5 centimeters

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