In the given figure, the angles $\angle B A Q=\angle C P Q=\angle C B Q=\frac{\pi}{2}$; and the lengths $Q A=3$ units, $A B=$ 4 units, and $B C=1$ unit. What is the length of $P Q$ ?

Consider a simple pendulum undergoing simple harmonic motion with a time period $T$, and a fixed amplitude $\theta_0$ of angular oscillation. Its angular momentum about the point of suspension exhibits an oscillatory behaviour with an amplitude $A$. Which of the following relations between $A$ and $T$ is correct?