Question

In an experiment to determine the period of oscillation of a loaded spiral spring,the equation of a simple harmonic oscillator $$a={-}(k/m)×$$,where the symbols have their usual meaning,was used.write down the equation for the angular frequency $\omega$ in terms of k and m,the effective mass of the system

Answer 1

Answer on Question #59258-Physics-Mechanics-Relativity

In an experiment to determine the period of oscillation of a loaded spiral spring, the equation of a simple harmonic oscillator $a = -\left(\frac{k}{m}\right)x$, where the symbols have their usual meaning, was used. Write down the equation for the angular frequency $\omega$ in terms of $k$ and $m$, the effective mass of the system

Answer

$$a = \ddot{x} = -\left(\frac{k}{m}\right)x \rightarrow \ddot{x} + \left(\frac{k}{m}\right)x = 0$$

The equation of a simple harmonic oscillator is

$$\ddot{x} + \omega^2 x = 0$$

Thus, the equation for the angular frequency $\omega$ in terms of $k$ and $m$ is

$$\omega = \sqrt{\frac{k}{m}}$$

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