Answer
(a) $T = 1.4~s$
(b) $A = 0.30~m$
Work Step by Step
(a) We can find the period as:
$T = 2\pi~\sqrt{\frac{m}{k}}$
$T = 2\pi~\sqrt{\frac{1.0~kg}{20~N/m}}$
$T = 1.4~s$
(b) We can find the amplitude as:
$A = \sqrt{x^2+\frac{v^2}{\omega^2}}$
$A = \sqrt{x^2+\frac{v^2}{(k/m)}}$
$A = \sqrt{(0.20~m)^2+\frac{(-1.0~m/s)^2}{(20~N/m)/(1.0~kg)}}$
$A = 0.30~m$
