Question

A force of 30 N stretches a vertical spring 15 cm. What mass must be suspended from the spring so that the system will oscillate with a period π/4 s?

Answer 1

Dear Student
$$\begin{gathered} F=kx \\ k=\frac{F}{x}=\frac{30}{15\times {10}^{-2}m}=200N/m \\ Nowfrequencyofoscillationsis \\ f=\frac{\omega }{2\pi }=\frac{1}{2\mathrm{\pi }}\sqrt{\frac{k}{m}} \\ m=\frac{k}{4{\mathrm{\pi }}^2{\mathrm{f}}^2}=\frac{200}{4{\mathrm{\pi }}^2{{\displaystyle \frac{\mathrm{\pi }}{16}}}^2}=\frac{200}{{{\displaystyle \frac{\mathrm{\pi }}{4}}}^4}=\frac{800}{{\mathrm{\pi }}^4}=8.23Kg \end{gathered}$$
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