What makes a source "ideal" as a current source. A practical source is a Norton equivalent — a current source with a shunt output impedance. It approaches the ideal current source when that output impedance becomes infinite, so that the current delivered is independent of whatever load is connected:

\(Z_{out}\to\infty\)

So the question is really: at what frequency does the impedance seen at A–B become infinite?

Step 1 — find the output impedance. Kill the independent source by shorting it. Looking back into A–B, the capacitor sits directly across the terminals, and the inductor also reaches those terminals through the short. The two are therefore in parallel:

\(Z_{out}=\dfrac{Z_LZ_C}{Z_L+Z_C}=\dfrac{(j\omega L)\left(\dfrac{1}{j\omega C}\right)}{j\omega L+\dfrac{1}{j\omega C}}=\dfrac{j\omega L}{1-\omega^{2}LC}\)

Step 2 — make it infinite. The denominator must vanish:

\(1-\omega^{2}LC=0 \quad\Longrightarrow\quad \omega_0=\dfrac{1}{\sqrt{LC}}\)

This is parallel resonance — the inductive and capacitive currents are equal and opposite, they circulate entirely within the LC loop, and none is drawn from outside. An ideal parallel LC at resonance is an open circuit.

Step 3 — substitute the values.

\(\omega_0=\dfrac{1}{\sqrt{\left(\tfrac{1}{16}\right)(1)}}=\dfrac{1}{\tfrac{1}{4}}=4\ \text{rad/s}\)

which is option 4.

Where the distractors come from. Option 3, 16 rad/s, is what you get by forgetting the square root — that is \(1/LC\), which has the units of ω², not ω. Option 1 would need LC = 1. Option 2, ω = 0, is the DC case, where the inductor is a short and the capacitor an open — the output impedance is then zero, which is the condition for an ideal voltage source, the exact opposite of what is asked.

The dual worth remembering. Series resonance makes the impedance minimum (a short at the terminals) and so approximates an ideal voltage source; parallel resonance makes it maximum and so approximates an ideal current source. Both occur at the same \(1/\sqrt{LC}\) — it is the topology, not the frequency, that decides which behaviour appears.

Hence, the circuit acts as an ideal current source at 4 rad/sec.