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A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency ω0. An external force F(t) proportional to cos ωt (ω ≠ ω0) is applied to the oscillator. The displacement of the oscillator will be proportional to
- 1 / [m(ω0² + ω²)]
- 1 / [m(ω² - ω0²)]
- m / (ω0² - ω²)
- m / (ω0² + ω²)
Correct answer: 1 / [m(ω² - ω0²)]
Solution
The steady-state amplitude of a driven oscillator is F0/[m(omega0^2 - omega^2)], so the displacement is proportional to 1/[m(omega^2 - omega0^2)] (the sign is just a phase). The stored choice puts m in the numerator, which is wrong; mass must appear in the denominator.
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