The LC Oscillator
Now let us analyze the oscillations of a resistance less LC circuit, proceeding exactly as we just did for the block-spring oscillator. The total energy V present at any in which UB is the energy stored-in the magnetic field of the inductor and U is the energy stored in the electric field of the capacitor. Since we have assumed the circuit resistance to be zero, no energy is transferred to thermal energy and U remains constant with time. In more formal language, must be zero. This leads to However With these substitutions,
This is the differential equation that describes the oscillations of a resistance less LC circuit. Equations are exactly of the same mathematical .