A smooth semicircular wire track of radius R is fixed in a vertical plane. One end of a massless spring of natural length 3R/4 is attached to the lowest point O of the wire track. A small ring of mass m which can slide on the track is attached to the other end of the spring. The ring is held stationary at point P such that the spring makes an angle 60° with the vertical. Spring constant K = mg / R. The spring force is
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CP = CO = R
∠ ∠ CPO = ∠ ∠ POC = 60 o
Thus Δ Δ OCP is an equilateral Δ Δ
∴ ∴ OP = R
∴ ∴ Extension = R – natural length of spring
= R - 
Thus spring force = kx = 
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