I have been looking for this for quite some time now. A simple pendulum behaves in SHM. Let's put that pendulum in an upward accelerating elevator. The component of the force that acts in SHM $(\text{mg}\sin\theta)$ still stays the same in my head.
However, websites and books tell me to use $m(g+a)\sin\theta$ where $a$ is the acceleration of the elevator.
I tried to look up Free Body Diagrams, but I can't find any for the case of accelerating frames. Can someone explicitly prove this without using the flimsy argument of "Think it's a noninertial frame with a new effective g"?