# Chapter 14 - Oscillations - Exercises and Problems: 12

$k = 5.48~N/m$

#### Work Step by Step

We first find the period as: $T = \frac{time}{cycles}$ $T = \frac{12.0~s}{10~oscillations}$ $T = 1.20~s$ We then find the spring constant as: $T = 2\pi~\sqrt{\frac{m}{k}}$ $k = \frac{(2\pi)^2~m}{T^2}$ $k = \frac{(2\pi)^2~(0.200~kg)}{(1.20~s)^2}$ $k = 5.48~N/m$

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