Answer
(a) $L = 7.5~m$
(b) $v_{max} = 0.45~m/s$
Work Step by Step
(a) We can find the length of the chain as:
$T = 2\pi~\sqrt{\frac{L}{g}}$
$L = \frac{T^2~g}{(2\pi)^2}$
$L = \frac{(5.5~s)^2(9.80~m/s^2)}{(2\pi)^2}$
$L = 7.5~m$
(b) We can find the amplitude of the motion as:
$\frac{A}{L} = sin(\theta)$
$A = L~sin(\theta)$
$A = (7.5~m)~sin(3.0^{\circ})$
$A = 0.39~m$
We can find the maximum speed as:
$v_{max} = A~\omega$
$v_{max} = A~\sqrt{\frac{g}{L}}$
$v_{max} = (0.39~m)~\sqrt{\frac{9.80~m/s^2}{7.5~m}}$
$v_{max} = 0.45~m/s$