Exercise · ZW-HARMONIC-OSCILLATOR-005 · ★☆☆ Basic
Solve \(y''+4y=0\), \(y(0)=0\), \(y'(0)=6\).
Choose one option.
Show answer
- B. \(y=3\sin2t\)
Explanation
\(y(0)=0\) gives \(c_1=0\); \(y'(0)=2c_2=6\) gives \(c_2=3\). One must divide by \(\omega\).
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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