Suppose you are in an elevator which oscillates vertically with a frequency $\nu$. How will we find the time dilation in this oscillating reference frame ? If the lift is accelerating upward or downward with a constant acceleration, time inside the elevator is given by $t'=t_{0}\,(1+gh/c^2)$. I want to know, How to generalize this equation for a non constant acceleration (i.e an oscillating frame of reference)?