Answer
(a) $T = 0.50~s$
(b) $A = 5.5~cm$
(c) $v_{max} = 0.69~m/s$
(d) $E = 0.048~J$
Work Step by Step
(a) $T = \frac{1}{f}$
$T = \frac{1}{2.0~Hz}$
$T = 0.50~s$
(b) We can find the angular frequency as:
$\omega = 2\pi~f$
$\omega = (2\pi)~(2.0~Hz)$
$\omega = 12.57~rad/s$
We can find the amplitude as:
$A = \sqrt{x^2+\frac{v^2}{\omega^2}}$
$A = \sqrt{(0.050~m)^2+\frac{(-0.30~m/s)^2}{(12.57~rad/s)^2}}$
$A = 0.055~m = 5.5~cm$
(c) We can find the maximum speed as:
$v_{max} = A~\omega$
$v_{max} = (0.055~m)(12.57~rad/s)$
$v_{max} = 0.69~m/s$
(d) We can find the total energy in the system as:
$E = \frac{1}{2}mv_{max}^2$
$E = \frac{1}{2}(0.200~kg)(0.69~m/s)^2$
$E = 0.048~J$
