In LC oscillations, energy is constantly being exchanged between the inductor and the capacitor. As the capacitor charges, it stores energy in the electric field. As it discharges, the energy is released and stored in the magnetic field of the inductor. This back-and-forth exchange of energy allows the oscillations to continue.
Energy conservation is a fundamental principle in physics, and it applies to LC oscillations as well. The total energy in an LC oscillator remains constant, with the energy being continuously converted between electric and magnetic forms.
Yes, the energy in an LC oscillator can be dissipated through resistance in the circuit. This is known as damping and it causes the amplitude of the oscillations to decrease over time. In an ideal LC circuit with no resistance, the energy would continue to oscillate indefinitely.
The energy in an LC oscillator is directly related to SHM. As the capacitor and inductor exchange energy, the motion of the system follows a sinusoidal pattern, just like in SHM. The rate of energy exchange also follows a simple harmonic function, with the energy reaching its maximum at the equilibrium point and decreasing to zero at the maximum displacement.
The energy in an LC oscillator is directly proportional to the square of the voltage and inversely proportional to the inductance and capacitance. This means that changes in either the inductance or capacitance will affect the amplitude and frequency of the oscillations. A larger inductance or capacitance will result in a larger amount of energy being stored and a slower oscillation frequency, while a smaller inductance or capacitance will result in a smaller amount of energy and a faster oscillation frequency.