## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

(a) $T = 0.50~s$ (b) $A = 5.5~cm$ (c) $v_{max} = 0.69~m/s$ (d) $E = 0.048~J$
(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: $E = \frac{1}{2}mv_{max}^2$ $E = \frac{1}{2}(0.200~kg)(0.69~m/s)^2$ $E = 0.048~J$