2.2 For the equation   \(\ddot{x} + 2 \gamma \dot{x} + \omega^2 x = 0\) , there are three qualitatively different solutions for \(\)\(x\), corresponding to the cases (i) \(\gamma > \omega\), (ii) \(\gamma = \omega\), (iii) \(\gamma<\omega\). These three cases correspond to the over-damped, critically damped, and under-damped scenarios. By recalling how we defined \(\gamma\), which case corresponds to which condition?

2.3 Solve the equations for over-damped and critically damped cases. There will be two arbitrary constants in both cases as we are dealing with a second-order differential equation, and these can be determined from the initial conditions. Sketch their corresponding plots of \(x\left(t\right)\) on the same graph.