Exercise · ZW-HARMONIC-OSCILLATOR-009 · ★★★ Advanced
Two oscillators have the same \(m\) and \(k\) but are released with different initial conditions. What is true?
Choose one option.
Show answer
- C. Same period, amplitudes may differ
Explanation
The period \(2\pi\sqrt{m/k}\) depends only on \(m\) and \(k\); the amplitude depends on \(y(0)\) and \(y'(0)\).
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-003 A mass m=1 on a spring with k=4 oscillates without damping. What is the period T?
- ZW-HARMONIC-OSCILLATOR-004 Solve y''+25y=0, y(0)=2, y'(0)=0.
- ZW-HARMONIC-OSCILLATOR-005 Solve y''+4y=0, y(0)=0, y'(0)=6.
- 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…