#### Answer

(a) The period is 4.00 seconds.
(b) The period is 5.66 seconds.
(c) The period is 2.83 seconds.
(d) The period is 4.00 seconds.

#### Work Step by Step

We can find an expression for the original period as:
$T = 2\pi~\sqrt{\frac{L}{g}} = 4.00~s$
(a) Since the period does not depend on the mass, the period is still 4.00 seconds.
(b) $T' = 2\pi~\sqrt{\frac{2L}{g}}$
$T' = \sqrt{2}\times ~2\pi~\sqrt{\frac{L}{g}}$
$T' = \sqrt{2}~T$
$T' = \sqrt{2}~(4.00~s)$
$T' = 5.66~s$
(c) $T' = 2\pi~\sqrt{\frac{L/2}{g}}$
$T' = \frac{1}{\sqrt{2}}\times ~2\pi~\sqrt{\frac{L}{g}}$
$T' = \frac{1}{\sqrt{2}}~T$
$T' = \frac{1}{\sqrt{2}}~(4.00~s)$
$T' = 2.83~s$
(d) Since the period does not depend on the amplitude, the period is still 4.00 seconds.