Amplitude-modulated (AM) radios use an oscillator operating at \(455 \mathrm{kHz}\) to demodulate the received signal. This frequency is called the intermediate frequency or IM. Your task is to design an \(L C\) oscillator that produces a sinusoid that has a \(5-\mathrm{V}\) peak output and runs at the IM frequency.

(a) Write the differential equation that determines the oscillator's output taken across the capacitor.

(b) Use MATLAB to solve the equation and plot the output. Verify that the amplitude and frequency are correct.

(c) Build the circuit in Multisim, and using a transient display, validate the output. Use a follower to isolate the \(L C\) circuit.