Exercise · ZW-HARMONIC-OSCILLATOR-002 · ★☆☆ Basic
For \(4y''+16y=0\), what is the angular frequency \(\omega\)?
Choose one option.
Show answer
- C. \(2\)
Explanation
Here \(m=4\) and \(k=16\), so \(\omega=\sqrt{16/4}=2\). Answering \(4\) forgets the square root.
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
- ZW-HARMONIC-OSCILLATOR-001 A mass m=1 attached to a spring with k=9 satisfies my''+ky=0. Find the angular frequency ω.
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- ZW-HARMONIC-OSCILLATOR-004 Solve y''+25y=0, y(0)=2, y'(0)=0.
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- ZW-HARMONIC-OSCILLATOR-006 An oscillator moves as y=3cos 2t+4sin 2t. What is its amplitude?
- ZW-HARMONIC-OSCILLATOR-007 A mass m=2 on a spring with k=8 starts with y(0)=1, y'(0)=4. What is the amplitude?
- ZW-HARMONIC-OSCILLATOR-008 The spring is replaced by one with k four times larger, with the same m. What happens to the angula…
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