Exercise · ZW-HARMONIC-OSCILLATOR-010 · ★★★ Advanced
With \(g=10\), a mass stretches a spring a length \(0.1\) at equilibrium. Then it oscillates without damping. What is \(\omega\)?
Choose one option.
Show answer
- B. \(10\)
Explanation
At equilibrium \(mg=kL\), so \(k/m=g/L=100\) and \(\omega=\sqrt{100}=10\). The value \(100\) is \(\omega^2\).
Review the concept: Harmonic oscillator
Model of a mass \(m\) attached to a spring of constant \(k\), with no friction or external force, whose position \(y(t)\) oscillates with angular frequency \(\omega\) about equilibrium.
\[my''+ky=0,\qquad \omega=\sqrt{k/m}\]
More practice problems: harmonic oscillator
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