All Problems

Mechanical Oscillations

Problem 4.86

The forced harmonic oscillations have equal displacement amplitudes at frequencies ω1=400 s−1\omega_{1}=400 \mathrm{~s}^{-1} and ω2=600 s−1\omega_{2}=600 \mathrm{~s}^{-1} Find the resonance frequency at which the displacement amplitude is maximum.

Reveal Answer
ωres=(ω12+ω22)/2=5.1⋅102 s−1\omega_{r e s}=\sqrt{\left(\omega_{1}^{2}+\omega_{2}^{2}\right) / 2}=5.1 \cdot 10^{2} \mathrm{~s}-1
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