A simple pendulum and a mass hanging on a spring both have a period of $1$ s when set into small oscillatory motion on Earth. They are taken to the moon $\backslash (\backslash$left$($g$\_\{$m o o n$\}=1\mathrm{.}67\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash$right$)\backslash ).$ Which of the following statements is true about the periods of the two objects on the moon compared to their periods on Earth?

Both are the same.

The period of the mass on the spring becomes longer; that of the pendulum keeps the same.

The period of the pendulum becomes shorter; that of the mass on the spring keeps the same.

The period of the mass on the spring becomes shorter; that of the pendulum keeps the same.

The period of the pendulum becomes longer; that of the mass on the spring keeps the same.