\Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the …

To circumvent this problem, let's apply the Resonance Exponential Response Formula: since p(s) = s2 +!2 n, p0(s) = 2s and p0(i!n) = 2i!0, so tei!nt zp = A : 2i!n

The notion of pure resonance is easy to understand both mathematically and physically, because frequency matching characterizes the event. This ideal situation never happens in the physical world, …

We can regard a resonance as a setting where there is a relatively large response. Here, the distance to resonance is b and the resonance described by the pendulum Hamiltonian.

In general, a “resonance” means that an amplitude becomes very large. In this case, it is the current through the circuit that becomes very large at the resonance frequency.

Summary of important concepts for series resonance: Capacitive and inductive reactances are equal. Total impedance is a minimum and is resistive. The current is maximum. The phase angle between …

The first observation is that at resonance, the voltage across the reactances can be larger, in fact much larger, than the voltage across the resistors R. In other words, this circuit has voltage gain.