A mass m is connected to a spring with spring constant k, giving it a natural angular frequency ω0. If an external driving force varying as cos(ωt) acts on the system, the oscillator’s displacement will be proportional to

1/(m(ω0² + ω²))
1/(m(ω0² - ω²))
1/(m(ω0² + ω²)²)
1/(m(ω0² - ω²)²)

Correct answer: 1/(m(ω0² - ω²))

Solution

For a forced oscillator (neglecting damping), steady-state displacement amplitude is proportional to 1/(m*(w0^2 - w^2)).

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