1. The problem statement, all variables and given/known data I have to find what angle a pendulum stops being simple harmonic motion experimentally and if possible theoretically. 2. Relevant equations T=2pi√(L/g)  d2θ/dt2+(g/r)sinθ=0  dθ/dt=√((2g(cosθ-cosψ))/L) where phi = theta initial  T = 4*∫oψdθ/  3. The attempt at a solution My first thought was to measure the period at intervals and compare that to the small angle approximation formula T=2pi√(L/g). After all a pendulum would be SHM if the period followed that formula for all angles right? So what we did was get a rigid pendulum and construct an board marked with angles at intervals of 5 degrees to place behind the pendulum. Using a photogate we measured the period from 5 degrees to 60 degrees at 5 degree increments. I'm sure period is key to what my professor wants us to find, but he did tell me my approach was wrong. So comparing true period to the period equation  is a no go. So this is where I need help. What do I do with the period to show at a certain angle that pendulum motion is no longer SHM? The above question is what I want answered most of all, but also on the theoretical side of things I started with equation  and derived it to equation  which I solved for T giving me equation . Now this appears to be right equation for T from looking at the graph. As theta deceases to 0, T is the same as T from equation . And as theta increases, T increases at an increasing rate. At 90 degrees I calculated equation  to be 15.3% off assuming equation  is accurate. Now trying to find the equation for T on the internet leads me to believe that it involves an elliptical integral and that just goes right over my head. My calc knowledge stops at calc 2 for now. So I assume my equation is just completely wrong?