Question

Consider an ideal LC circuit consisting of an (initially charged) capacitor C and a solenoid L. Compare an LC circuit to a spring with force Fspring= -kx=Ma where x(t) is the displacement of the spring at time t and the acceleration is a. Kirchhoff’s circuit laws applied to the LC circuit states that Vl + Vc = 0.

Let i=i(t) be the current in the circuit and q=q(t) is the magnitude of the instantaneous charge on either capacitor plate. Consider a simple mechanical oscillator ( a spring with mass M and spring constant k)...

a) Write the differential equation for q(t) for the LC circuit and the differential equation for x(t) of the spring.

b) Write the solutions of the following equations for which q(0)=Q0 and x(0)=A respectively.

x(t)

q(t)

c) Find KE(t) and PE(t) for the LC circuit and prove that the total energy in the circuit is constant

Answer 1