torsional pendulum, frequency of oscillation (f) is defined as,f = 1/2π √k/IHere k is the force constant and I is the rotational inertia of the body.For moon gʹ = g/6. But the frequency is independent of g. It depends on k and I, which are always constant for a given mass and cord. So the frequency does not change.For simple pendulum,f = 1/2π √g/lHere g is the acceleration due to gravity and l is length of pendulum. For moon gʹ = g/6. So the frequency of oscillation depends up on acceleration due to gravity g. It changes when you take the simple pendulum to moon due to gravitational acceleration and it becomes,f = 1/2π √g/6l.For simple block oscillator, frequency of oscillation (f) is defined as,f = 1/2π √k/mHere k is the force constant and m is the mass of block.From the above equation f = 1/2π √k/m, we observed that the frequency of oscillation f is independent of acceleration due to gravity g. Therefore it also does not change.For physical pendulum, frequency of oscillation (f) is defined as,f = 1/2π √Mgd/IHere M is the mass of pendulum, g is the acceleration due to gravity, d is the distance from the pivot to the center of mass and I is the rotational inertia of body.Since the frequency of oscillation depends up on g, therefore it also changes and it becomes,f = 1/2π √Mgd/6l

As the time period of a simple pendulum and a physical pendulum depends on the acceleration due the gravity, the time period of these pendulums changes when they are taken to the moon.