Exercise · ZW-HARMONIC-OSCILLATOR-007 · ★★☆ Intermediate
A mass \(m=2\) on a spring with \(k=8\) starts with \(y(0)=1\), \(y'(0)=4\). What is the amplitude?
Choose one option.
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- D. \(\sqrt5\)
Explanation
\(\omega=\sqrt{8/2}=2\) and \(y=\cos2t+2\sin2t\), with amplitude \(\sqrt{1+2^2}=\sqrt5\). Using \(4\) without dividing by \(\omega\) would give \(\sqrt{17}\).
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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