A light, ideal spring of spring constant k=40N/m is first laid horizontally on a frictionless table with one end fixed. A 0.50kg block is attached to the free end and held so that the spring is at its natural length, then released from rest.
(1) (a) Determine the position(s) of translational equilibrium for the block in the horizontal arrangement, and explain how you identified the equilibrium point(s).
(2) The same spring–block system is now suspended vertically with the upper end of the spring fixed and the block again attached to the lower end.
(3) (b) Calculate the numerical value of the spring’s extension Δℓ when the block is in static equilibrium in the vertical orientation.
(4) (c) Compare the equilibrium locations found in parts (a) and (b). Explain why the addition of Earth’s gravitational force changes the location of equilibrium but does not alter the period of small oscillations about that new equilibrium.