Electric pendulum

As shown above, a charged particle is hanging on the top of two parallel plates. A voltage of \(V\) generates a uniform electric field inside the plates. If we lift up the charged particle to the point \(x\) and then let it go, the charged particle oscillates between \(x\) and \(z\) with \(y\) the center point of the oscillation. Which of the following statements is correct? (Ignore gravity, air resistance and the generation of electromagnetic waves.)

a) The electric potential at the point \(x\) is greater than that at the point \(y.\)

b) The period of the oscillation decreases as the voltage \(V\) increases.

c) The magnitude of the electric force acting on the charged particle at the point \(x\) is greater than that at the point \(y.\)

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