Answer
$(a)\space 0.5\space m$
$(b)\space 1.19\space m/s$
Work Step by Step
(a) When the mass is at the amplitude, kinetic energy becomes zero & only potential energy exists. So we can write,
$E_{T}=\frac{1}{2}KA^{2}$ ; Let's plug known values into this equation.
$7.69\space J=\frac{1}{2}\times 63.7\space N/m\times A^{2}$
$0.5\space m = A\space (Amplitude)$
(b) We know that,
$V_{max}=A\omega=0.5m\times 2.38\space m/s$
$V_{max}=1.19\space m/s$
Maximum speed = 1.19 m/s
