If a clock is swinging on a pendulum (assume it's on some massive object with gravity) what happens when that system is moving at relativistic speeds? To an inertial observer, on the back-swing (i.e. opposite the direction of movement of the system) the pendulum has a lower ("absolute") velocity than on the forward swing. The clock should experience less time dilation on the back-swing, and that should register as a different number of 'ticks' on the clock, but that can't be because then the 'moving' observer would notice that too!
Is the length (duration) of each swing different to cancel out that effect, and what causes the change in duration: (is it because the weight/bob is relativistically more massive on the forward swing?)
I don't know too much, so please keep the explanation simple!
Please note, gravity should not play much of a role here. I could ask the same question with an oscillating tuning fork to avoid most gravitational complications.