Answer
(a) $1.5$ Hz, (b) $0.34$ s.
Work Step by Step
The simple harmonic motion equation is $x(t)=Acos(\omega t)$. Angular frequency and frequency are related using the equation $$\omega=2\pi f$$ Since $\omega=\frac{2\pi}{0.58s}$, the period must be $\frac{1}{0.58s}=1.5s$. The time it takes to travel from the positive amplitude (7.8cm) to $x=-7.8cm$ (the negative amplitude) is one-half of the period, since the mass travels $4A$ in one cycle. This time is $(0.68s)/2=0.34s$.
