Answer
(a) $0.58s$ (b) $0.15s$
Work Step by Step
The simple harmonic motion equation is $x(t)=Acos(\omega t)$. Angular frequency and frequency are related using the equation $$\omega=\frac{2\pi}{T}$$ Since $\omega=\frac{2\pi}{0.58s}$, the period must be $0.58$ seconds. The time it takes to travel from the amplitude to $x=0$ is one-fourth of the period, since the mass travels $4A$ in one cycle. This time is $(0.58s)/4=0.15s$.
