The oscillation

The oscillation of a mechanical oscillator can be used to measure weight. A body of unknown weight is suspended on a spring with a stiffness of 20 N times m. The resulting oscillator oscillates with a frequency of 1.6 Hz. Find the weight of the body.

Correct answer:

m =  0.1979 kg

Step-by-step explanation:

$$\begin{gathered} f=1.6\text{ Hz } \\ k=20\text{ Nm } \\ g=9.81{\text{m/s}}^2 \\ f={\displaystyle \frac{1}{2\pi }}\cdot \sqrt{{\displaystyle \frac{k}{m}}} \\ 2\pi \cdot f=\sqrt{{\displaystyle \frac{k}{m}}} \\ 4{\pi }^2{f}^2=k\mathrm{/}m \\ m={\displaystyle \frac{k}{4{\pi }^2\cdot f^2}}={\displaystyle \frac{20}{4\cdot 3.1416^2\cdot 1.6^2}}=0.1979\text{ kg} \end{gathered}$$

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