6:33 AM
Ah ok; my second method is used energy conservation which is getting me a different answer. Here goes -
Initial KE and final KE (at the extreme position) is both zero
Let us split the displacement of the bob into two components, a horizontal component $w$ and a vertical component $h$
Now since we are in a non-inertial frame of reference a pseudo-force is present
acting on the bob towards the left (car is accelerating towards the right)
Total work done = change in energy
Work done by gravity + work done by pseudo-force = change in PE (since change in KE = 0)
assuming mass of bob to be $m$
$\frac{a}{2g} = \frac{h}{w}$
$tan(\theta) = \frac{w}{h}$
$\theta = arctan(\frac{2g}{a})$
so where am I going wrong?
It's probably something silly but I just can't figure out what
I wrote something wrong in the above steps but the answer is still different; lemme repeat the last few lines