Consider the system shown in Fig. 1. Two parallel plates locate with a gap g0 initially. The lower plate is used as a ground electrode. The upper plate is used as a driving electrode for applying voltage. A spring with spring constant k is attached to the upper plate and unstretched when the gap between the two plates is g0. As applying voltage, the two plates will be attracted to each other by electrostatic force. Meanwhile, the spring will be elongated and offer an elastic force to resist electrostatically driving. Therefore, due to the balance of elastic and electrostatic forces, the gaps will be a relation of applying voltages. However, as applying voltages increasing, the electrostatic forces will increase nonlinearly. For a critical applying voltage, the electrostatic force will become a huge force that cannot be balanced by elastic force. Therefore the upper plate will snap move to the lower plate. This phenomenon is called “pull-in”. Please discuss the dynamics of pull-in phenomena when (a) the system is in a vacuum.

k V