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Illustration Amplitude-Frequency Graph of a Forced Damped Oscillator

Amplitude-Frequency Graph of a Forced Damped Oscillator
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Three different amplitudes \(A_0\) of a forced harmonic oscillation as a function of the excitation frequency \(\omega\) - with different damping constants \(b\). The \(y\)-axis intercept gives the ratio of the excitation amplitude \(F_0\) to the spring constant \(D\):$$ F_{\text{ext}} ~=~ F_0 \, \cos(\omega\,t) $$

Here \(\omega_0 = \sqrt{ \frac{D}{m} }\) is the natural frequency of the oscillator with \(m\) e.g. as the mass of a body hanging on a spring.