Exercise · ZW-HARMONIC-OSCILLATOR-006 · ★★☆ Intermediate
An oscillator moves as \(y=3\cos2t+4\sin2t\). What is its amplitude?
Choose one option.
Show answer
- C. \(5\)
Explanation
Write \(y=A\cos(2t-\varphi)\) with \(A=\sqrt{3^2+4^2}=5\). The amplitudes do not simply add.
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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