Answer
(a) $11\frac{rad}{s}$
(b) $0.34\frac{m}{s}$
(c) $0.57s$
Work Step by Step
(a) We know that
$\omega=\sqrt{\frac{K}{m}}$
We plug in the known values to obtain:
$\omega=\sqrt{\frac{69}{0.57}}=11\frac{rad}{s}$
(b) We can find $v_{max}$ as
$v_{max}=A\omega$
We plug in the known values to obtain:
$v_{max}=(0.031)(11)=0.34\frac{m}{s}$
(c) The time period can be determined as
$T=2\pi\sqrt{\frac{m}{K}}$
$\implies T=2\pi\sqrt{\frac{0.57}{69}}=0.57s$
