  The prediction made by L. O. Chua 45+ years ago (see: IEEE Trans. Circuit
Theory (1971) 18:507-519 and also: Proc. IEEE (2012) 100:1920-1927) about the
existence of a passive circuit element (called memristor) that links the charge
and flux variables has been confirmed by the HP lab group in its report (see:
Nature (2008) 453:80-83) on a successful construction of such an element. This
sparked an enormous interest in mem-elements, analysis of their unusual
dynamical properties (i.e. pinched hysteresis loops, memory effects, etc.) and
construction of their emulators. Such topics are also of interest in mechanical
engineering where memdampers (or memory dampers) play the role equivalent to
memristors in electronic circuits. In this paper we discuss certain properties
of the oscillatory memristive circuits, including those with mixed-mode
oscillations. Mathematical models of such circuits can be linked to the
Newton's law $\phi''\!-\!F(t,\phi,\phi')/m=0$, with $\phi$ denoting the flux or
charge variables, $m$ is a positive constant and the nonlinear non-autonomous
function $F(t,\phi,\phi')$ contains memory terms. This leads further to scalar
fourth-order ODEs called the jounce Newtonian equations. The jounce equations
are used to construct the $RC$+op-amp simulation circuits in SPICE. Also, the
linear parallel $G$-$C$ and series $R$-$L$ circuits with sinusoidal inputs are
derived to match the $rms$ values of the memristive periodic circuits.
