One end of a massless coil spring is suspended from a rigid ceiling. It is found that when a 3.3 kg mass is suspended from it the spring stretches 105 mm when the mass comes to rest.

Question

(a) What is the spring constant for the spring?
(b) If the mass is then pulled down an additional 165 mm (by hand) and released from rest at that point, what will be the speed of the mass when it passes through the spring-mass rest position (this is where the spring was stretched 100.mm by the stationary mass).

Answer 1

(a) k = Weight/Deflection
= M g/(0.105 m) = 308 N/m

(b) V at that time will be whatever makes the kinetic energy equal to the spring potential energy at maximum displacement from the equilibrium position. Refer spring potential energy to the equilbrium position.

(1/2)k X^2 = (1/2) M V^2

X = 0.165 m
M = 3.3 kg
Solve for V