A simple pendulum swings about the vertical equilibrium position with a maximum angular displacement of $5^\circ$ and period $T$. If the same pendulum is given a maximum angular displacement of $10^\circ$, then which of the following best gives the period of the oscillations?
A) $\displaystyle \frac{\ T}{2}$
B) $\displaystyle \frac{\ T}{\sqrt{2}}$
C) $T$
D) $2T$
A) $\displaystyle \frac{\ T}{2}$
B) $\displaystyle \frac{\ T}{\sqrt{2}}$
C) $T$
D) $2T$
For small angular displacements, the period of a simple pendulum is essentially independent of amplitude.