A parallel plate capacitor whose capacitance $C$ is $14 \mathrm{pF}$ is charged by a battery to a potential difference $V=12 \mathrm{V}$ between its plates. The charging battery is now disconnected and a porcelain plate with $k=7$ is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of _______ $\mathrm{pJ}.$

(Assume no friction)