#### Answer

(a) $T' = 2.0~s$
(b) $T' = 2.83~s$
(c) $T' = 2.0~s$

#### Work Step by Step

We can write an expression for the period $T$ of an oscillating pendulum.
$T = 2\pi~\sqrt{\frac{L}{g}} = 2.0~s$
(a) Since the period does not depend on the mass, the period of $T = 2.0~s$ remains the same.
(b) We can find the period $T'$ when the length is doubled.
$T' = 2\pi~\sqrt{\frac{2L}{g}}$
$T' = \sqrt{2}\times 2\pi~\sqrt{\frac{L}{g}}$
$T' = \sqrt{2}\times T$
$T' = (\sqrt{2})(2.0~s)$
$T' = 2.83~s$
(c) Since the period does not depend on the oscillation amplitude, the period of $T = 2.0~s$ remains the same.