A mass oscillates on the end of a spring, both on earth and on the moon. where is the period the greatest?

Draw a diagram to illustrate the problem as shown below.

m = mass of the object

x = displacement

k = spring constant

g = acceleration due to gravity.

The driving force of mg (weight) is opposed by the spring restoring force

of - kx.

The equation of motion is

mg - kx = m x''

or

x'' + (k/m) = g

For oscillatory motion, the homogeneous solution of the ODE yields

ω² = 2π/T = k/m

where

T = period of oscillation

ω = circular frequency

The period is T = 2π√ (m/k)

Answer:

Th period is independent of g, therefore the period will be the same on earth and the moon.