Amass 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)

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

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