Answer
The period of the pendulum on the new planet is less than one second.
The period of the mass-spring system on the new planet is equal to one second.
Work Step by Step
We can write the equation for the period of a pendulum:
$T_p = 2\pi~\sqrt{\frac{L}{g}}$
If $g$ increases, then the period of the pendulum decreases. Therefore, the period of the pendulum on the new planet is less than one second.
We can write the equation for the period of a mass-spring system:
$T_s = 2\pi~\sqrt{\frac{m}{k}}$
Even if $g$ changes, the period of the mass-spring system remains the same since the period is independent of $g$. Therefore, the period of the mass-spring system on the new planet is equal to one second.
