1. The problem statement, all variables and given/known data Hi all! I'm slightly confused about pendulums and simple harmonic motion. In my text book, it says that a pendulum only exhibits simple harmonic motion when the angle is small (<10 degrees). I was wondering why this is, using equations if possible. Without the math, I think this is the case because the part of the pendulum's motion that exhibits SHO is its horizontal displacement from the equilibrium position (i'm not sure about this though. Does the up/down motion also exhibit SHO or can the whole motion, not just the horizontal motion, be described as SHO) and in that case the restoring force can be approximated by the tangential force, which is -mgsinθ. And then only for small angles is sinθ≈θ, and so only then is the acceleration proportional to the displacement as in SHO... I really think this is wrong. 2. Relevant equations 3. The attempt at a solution I'm trying to find the acceleration of the pendulum bob at any point, and so far I have that the resultant force perpendicular to the velocity of the bob is 2mgcosθ-2mgcos(θmax) and the tangential force is mgsinθ, but i'm not even sure where I am going with this... I don't really get pedulums, so any help on this would be much appreciated!!!