Let $k$ be any constant, given $ \theta(0)=0$, $ \frac d{dt}\theta=0$ when $t=0$, t = ? if $ \theta = \frac \pi 2$ where $t$ represents time.
$ \frac{d^2}{dt^2}\theta = k\sin\theta $
How would I solve this problem in the simplest manner? This can be modeled with large angle pendulum or falling stick (of unifom thickness) falling from unstable equilibrium.
Since we can calculate the time taken by the blob from $ \pi/2 \text{ to } 0 $ ( or $ \pi $ ) shouldn't we able to calculate the time theoretically? Correct me if I'm mistaken.
Let the parameter be $ \theta(0)=\pi/2$, $ \frac {d\theta}{dt}=0$ when $t=0$, t = ? if $ \theta = \pi \text{( or 0) } $