A simple pendulum consisting of a small bob of mass $$m$$ attached to a massless inextensible string of length $$\ell = 2\ \text{m}$$, hanging vertically from the ceiling, is oscillating in a vertical plane with an angular amplitude $$\theta_m$$ such that the maximum tension in its string is three times the minimum tension in the string, so $$T_{\max}=3T_{\min}$$. The correct options are

A

The maximum tension in the string is $$T_{\max}=mg(3-2\cos\theta_m)$$

B

The maximum tension in the string is $$T_{\max}=\frac{9}{5}mg$$

C

The maximum velocity of the bob on its way is $$v_{\max}=3.96\ \text{m}/\text{s}$$

D

The angular amplitude $$\theta_m$$ lies in the range $$\frac{\pi}{4}<\theta_m<\frac{\pi}{3}$$