**Context**

You are given a simple AC LCR circuit (setup in that order, in series, depicted graphically as a square). The AC Voltage source in the circuit replicates the input energy from the sound waves hitting the glass. The inductor and capacitor replicate the resonance characteristics of the glass, and the resistor replicates the energy being converted by the glass as it vibrates. When the energy converted in the resistor is over 200J/s the glass can no longer support vibration and shatters.

**Given Values**

Vs = ?

L = 4H

C = 3 x 10^(-10)F

R = 50Ohms

**Questions**

(1) Find the resonant frequency (rad/sec and Hz) of the sheet of glass.

(2)Find the magnitude of the voltage across the resistor in the equivalent circuit, required to break the glass, at the resonant frequency.

(3) Find the magnitude of the voltage source in the equivalent circuit, required to break the glass at resonant frequency. Compare the last two values found.

(4) Using the voltages found above, find the gain (in dB, gain = 20log(Vout/Vin), where Vout is across the resistor) vs the frequency for the following points: 0.01 x w0, 0.1 x w0, w0, 10 x w0, 100 x w0 (where w0 is the resonant frequency.

(5) The clients plan to use that is only accurate to within +-20% of the desired frequency.

- How much sound power do they need to be sure to break the glass?

- At the worst case scenario (20% away from resonant frequency ) find the voltage magnitude and phase shift across each component; source, inductor, capacitor and resistor.

**Comments**

My answer for Q1 was 28,867.513 rad/s or 4,594.407Hz.

I am currently trying to determine the V(r) without being given the source voltage.. I haven't done it before without being given that variable.