Question

A vertical spring stretches 4.4 cm when a 14-g object is hung from it. The object is replaced with a block of mass 24 g that oscillates up and down in simple harmonic motion. Calculate the period of motion.

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Force constant of the spring = k

Mass of the first object hung from the spring = m₁ = 14 g = 0.014 kg

Amount the spring stretches due to the first object = X₁ = 4.4 cm = 0.044 m

m₁g = kX₁

(0.014)(9.81) = k(0.044)

k = 3.121 N/m

Mass of the second object attached to the spring = m₂ = 24 g = 0.024 kg

Time period of the oscillation of the second object on the spring = T

T = 0.55 sec

Time period of the simple harmonic oscillation of the 24 g object on the spring = 0.55 sec