Capacitor: Stores energy in an electric field. | Inductor: Stores energy in a magnetic field.

Angular Frequency ($\omega$): Measured in rad/s, represents the rate of change of the phase. | Frequency ($f$): Measured in Hz, represents the number of cycles per second. Relationship: $\omega = 2\pi f$.

Inductor: Opposes changes in current, acting as the restoring force. | Capacitor: Resists changes in voltage, providing the inertia.

Capacitor: $U_C = \frac{1}{2}CV_{max}^2$ | Inductor: $U_L = \frac{1}{2}LI_{max}^2$

Increasing L: Decreases the angular frequency ($\omega$). | Increasing C: Decreases the angular frequency ($\omega$).

The property of a circuit element that opposes changes in current, storing energy in a magnetic field.

The ability of a component to store energy in an electric field.

The rate of change of the phase of a sinusoidal waveform, measured in radians per second.

A type of periodic motion where the restoring force is directly proportional to the displacement, resulting in sinusoidal oscillations.

The maximum charge stored on the capacitor during the oscillation cycle.

Energy oscillates between the capacitor (electric field) and the inductor (magnetic field). Capacitor discharges, transferring energy to the inductor. The inductor then discharges, transferring energy back to the capacitor, repeating the cycle.

1. Equate the initial energy in the capacitor to the maximum energy in the inductor: $\frac{1}{2}CV_{max}^2 = \frac{1}{2}LI_{max}^2$. 2. Solve for $I_{max}$: $I_{max} = V_{max}\sqrt{\frac{C}{L}}$

1. Start with Kirchhoff's loop rule: $L\frac{dI}{dt} + \frac{q}{C} = 0$. 2. Substitute $I = \frac{dq}{dt}$: $\frac{d^{2}q}{dt^{2}} = -\frac{1}{LC}q$. 3. Recognize the SHM equation form: $\frac{d^{2}x}{dt^{2}} = -\omega^2x$. 4. Identify $\omega^2 = \frac{1}{LC}$, therefore $\omega = \frac{1}{\sqrt{LC}}$

1. Recognize that the charge oscillates with SHM. 2. Use the general form: $q(t) = q_{max}\cos(\omega t + \phi)$. 3. Determine $q_{max}$ (maximum charge). 4. Determine $\omega$ (angular frequency). 5. Determine $\phi$ (phase constant, often 0 if the capacitor is initially fully charged).

1. Identify the capacitance (C) and voltage (V) across the capacitor. 2. Use the formula: $U_C = \frac{1}{2}CV^2$. 3. Plug in the values of C and V to calculate $U_C$.