The oscillation

The oscillation of a mechanical oscillator can be used to measure weight. A body of the 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:

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

Try another example