# Chapter 10 - Problems - Page 400: 56

(a) The period of the motion is $0.90~s$ (b) The maximum speed is $0.56~m/s$

#### Work Step by Step

(a) We can find the spring constant $k$: $kd = mg$ $k = \frac{mg}{d}$ $k = \frac{(6.8~kg)(9.80~m/s^2)}{0.20~m}$ $k = 333.2~N/m$ We can find the period of the motion: $T = \frac{2\pi}{\omega}$ $T = 2\pi~\sqrt{\frac{m}{k}}$ $T = 2\pi~\sqrt{\frac{6.8~kg}{333.2~N/m}}$ $T = 0.90~s$ The period of the motion is $0.90~s$ (b) We can find the maximum speed: $v_m = A~\omega$ $v_m = A~\sqrt{\frac{k}{m}}$ $v_m = (0.080~m)~\sqrt{\frac{333.2~N/m}{6.8~kg}}$ $v_m = 0.56~m/s$ The maximum speed is $0.56~m/s$

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