What is the equation of motion for a resonating system?

The equation of motion for a resonating system is given by x(t) = A sin(ωt + φ).

In a resonating system, the object oscillates back and forth with a certain frequency. The equation of motion for such a system can be expressed as x(t) = A sin(ωt + φ), where x is the displacement of the object from its equilibrium position, A is the amplitude of the oscillation, ω is the angular frequency of the oscillation, t is time, and φ is the phase angle.

The angular frequency ω is related to the natural frequency of the system, which is the frequency at which the system oscillates without any external force. The natural frequency can be calculated using the equation f = 1/(2π√(L/C)), where L is the inductance and C is the capacitance of the system.

The amplitude A of the oscillation depends on the initial conditions of the system. If the system is initially displaced from its equilibrium position, the amplitude will be greater than if the system is initially at rest.

The phase angle φ represents the position of the object in its oscillation cycle at a given time. It is determined by the initial conditions of the system and the frequency of the oscillation.

In summary, the equation of motion for a resonating system is x(t) = A sin(ωt + φ), where x is the displacement of the object, A is the amplitude of the oscillation, ω is the angular frequency, t is time, and φ is the phase angle. The natural frequency of the system can be calculated using the equation f = 1/(2π√(L/C)).