Question

A ball of mass m kg hangs from a spring of spring constant k. the ball oscillates with a time period t

Answer 1

The time period of the oscillation is T = 2π√(m/k)

Given data;

Mass of the object = m

spring constant = k

For a spring we know that restoring force F = -kx

From the laws of motion, F = ma

=> ma = -kx

for an oscillatory system we know that a = -ω²x

=> m(-ω²x) = -kx

=> ω² = k/m

=> ω = √(k/m)

=> 2π/T = √(k/m)

=> T = 2π√(m/k)

Hence the time period of the oscillation is T = 2π√(m/k)