With L = 1, C = 0.0625 and R = 1, ωn = 4 rad/s and ζ = 0.125. The capacitor-voltage gain peaks near 3.94 rad/s; series-current magnitude peaks at 4 rad/s. The measured quantity matters. At zero resistance and exact natural frequency, a nonzero sine has no bounded sinusoidal steady state.
Make one fair comparison
Pin a 1 V sine at 1 rad/s. Change only frequency to 3.94, then 8 rad/s. Compare late capacitor voltage and current. Startup transients remain part of a finite recording.
Before moving a setting, write which signal you expect to change and why. A faster-looking curve alone does not explain the mechanism. Keep the initial state and all other settings visible in the pinned run.
Resonance depends on the output you ask about
For positive R, series-current magnitude reaches its maximum at 1/√(LC). Capacitor-voltage magnitude instead peaks at ωn√(1−2ζ²) only when 0<ζ<1/√2. With ζ=0.125, the voltage peak is around 3.94 rad/s rather than 4. A measured output includes its own scaling and frequency dependence; do not label every maximum simply as the natural frequency.
A short sine experiment contains the forced response and the initial transient. With zero resistance, the transient does not decay; at exact natural frequency the nonzero sinusoidal input produces growing oscillations and no bounded steady-state amplitude. Compare the end of matched-duration recordings and explain the assumptions before reading a peak as a frequency-response gain.
What to change next
Specify both the input and the measured output before quoting a resonant frequency. Compare capacitor voltage with current under identical excitation. If the record is too short for transients to decay, report that limitation instead of treating the visible maximum as a steady-state gain.
With L = 1, C = 0.0625 and R = 1, ωn = 4 rad/s and ζ = 0.125. The capacitor-voltage gain peaks near 3.94 rad/s; series-current magnitude peaks at 4 rad/s. The measured quantity matters. At zero resistance and exact natural frequency, a nonzero sine has no bounded sinusoidal steady state.
CHECK YOUR UNDERSTANDING: Must the largest capacitor-voltage response occur exactly at ωn = 1/√(LC)?
With L = 1, C = 0.0625 and R = 1, ωn = 4 rad/s and ζ = 0.125. The capacitor-voltage gain peaks near 3.94 rad/s; series-current magnitude peaks at 4 rad/s. The measured quantity matters. At zero resistance and exact natural frequency, a nonzero sine has no bounded sinusoidal steady state.