How to find the period of a simple pendulum in an elevator going up with an acceleration of $a$.

Don't just say, $T=2 \pi$ $\sqrt{ \frac l {g+a}}$

I want to know how the above equation is formed.

  • 2
    $\begingroup$ What do you think? $\endgroup$
    – CuriousOne
    Jun 2, 2015 at 2:59
  • 1
    $\begingroup$ I downvoted this because the answer is on this site and one 10 second search found it. $\endgroup$
    – user81619
    Jun 2, 2015 at 3:11
  • $\begingroup$ I searched you know but couldn't find anything helpful $\endgroup$
    – jessij
    Jun 2, 2015 at 3:14

1 Answer 1


Einstein's Equivalence Principle (also derivable I believe from Newton's laws) states that being in an accelerating frame of reference is indistinguishable from being under a gravitational force.

In particular, the mechanical laws in an accelerating frame of reference are the same as if a gravitational field of equivalent magnitude were added in the opposite direction to that of the acceleration.

So in your frame of reference accelerating upward at a in a standard gravitational field of g downward, we see that this is equivalent to a gravitational field of (g+a) downward.

So we can take any equation involving the local gravitational field g which applies in an inertial frame, and change g to (g+a), and this new version will apply in your accelerating frame.

  • $\begingroup$ Can you please, help me in deriving this using Newton's laws? $\endgroup$ Sep 22, 2017 at 8:42

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