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.
