an observer see's a system consisting of a spring and mass in SHM move past them and measures the period of oscillation to be T. What will a second observer riding with the system see the period as T as?
γ*proper time = time.
so the person moving along with the system is viewing the proper time, and therefore the person looking on from outside will be viewing the time that is INCREASED. so the person riding with the system will see a smaller period than the person observing the system from the outside.
That is what I came up with qualitatively. However the demon that was bothering me regarding this question is does length contraction come into play here to balance the equations out? I figure since T is measure in units of seconds I could just use the time dilation equation, but does the fact that one person see's the oscilliation moving a further distance than the other make a difference?
Is the idea that the person riding along with the system will perceive a shorter time of oscillation than the person watching in a different reference frame?