What is this strange harmonic content present in a resonant circuit output waveform?

Question

The following is an LC circuit excited at resonant frequency 15.915Hz (L=10mH, C=10mF.)

I would expect the output to have only the resonant frequency (constantly increasing in amplitude) since the AC source and the natural response are of the same frequency.

1. Why is there an underlying frequency of 100mHz?

2. Why is the amplitude not increasing continuously?

Both L and C are defined to have zero resistance (ESR.)

Answer 1

Your circuit has no damping (except the Rser=1m default parasitic of the inductor, or the Rpar=1/Gmin for the capacitor, if added), so what you see is not the "real" result. Since there is (virtually) no damping then there can be no damped oscillation, so the output should rise to infinity and, possibly, beyond. To correct the output you need to impose a tighter timestep. Here is how the output looks like for an increasing timestep of 1 s (no effect since it's less than 1/1024 points, by default), then for 1 ms, and then for 10 us (1 us will not be an improvement over 10 us):

If it stops at 1 kV amplitude it's because of the Rser=1m. If you set it to zero, it will do what you expect it to do. The reason has to do with how the SPICE engines calculate their timesteps and how very simple, linear circuits, such as this one, can influence it. TLDR: if it's simple and fast, the timestep shall not be constrained. Of course, the simulator tries to do what it can with the given input, so GIGO applies (which is your case: ideal voltage source, "pure" LC).

Answer 2

There may be something hidden with your voltage source if you are getting that result. Possibly LTSpice has created a little bit of series resistance or current limiting because, no-way would the output settle down to an 80 volt peak sinewave without this damping being present. Neither would the perturbations remain at a fairly constant amplitude up to the 50 second point in the plot.

Additionally, your excitation frequency is miscalculated at around the 7th decimal place but even that wouldn't cause the perturbations you see. To get what you see, the excitation frequency would need to be out by about 0.1 Hz so, double check that you didn't use 15.815 Hz instead of 15.915 Hz. In Micro-cap, to get anything like the same response as yours, I would need to drive the tuned circuit with a 0.1 Hz error and have series resistance of about 0.0005 Ω: -

Circuit simulated: -

But, if I discard the series damping resistor and slight error in the excitation frequency, the output waveform will do this (as expected): -

Notice that the waveform has peaked at +/- 10 kV after 200 seconds and, will continue in this fashion theoretically.