Swing Equation 

When a Fault occurs, Load Angle increases. When a Fault is cleared, Load Angle decreases. However, due to Inertia, it swings further. It makes a few more Swings before settling at Steady State.
The equation describing Swing of Rotor is called Swing Equation.
Swing is also called Oscillation or Hunting.
Swing Equation is derived using Accelerating Torque = J Alpha, where J is Moment of Inertia and Alpha is Angular Acceleration. We get Accelerating Torque = J d Omega R/dt. Multiplying both sides by Omega R, we get Swing Equation i.e. Pacc = M d square Delta / dt square. Where Accelerating Power = Mechanical Input Power - Electrical Output Power and M is Angular Momentum.
Using Swing Equation, Equal Area Criteria is derived and thus finding Critical Clearing Time.