In Search of Oscillatory Traces of the Internal Clock

An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by

Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...

Sleep is an essential physiological process vital to maintaining overall well-being. The reticular activating system (RAS), a network of neurons in the brainstem, regulates wakefulness and sleep. While it may seem passive, sleep consists of distinct cycles, each with its unique characteristics and functions. Two key sleep phases are non-rapid eye movement (NREM) and  rapid eye movement (REM).
NREM Sleep
NREM sleep comprises four progressive stages that seamlessly merge:

When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.

When a rigid body is hanging freely from a fixed pivot point and is displaced, it oscillates similar to a simple pendulum and is known as a physical pendulum. The period and angular frequency of a physical pendulum are obtained by using the small-angle approximation and drawing parallels with a spring-mass system. The small-angle approximation (sinθ=θ) is valid up to about 14°.
When dealing with complicated systems, the mass moment of inertia is an important parameter, as it...

The circadian—or biological—clock is an intrinsic, timekeeping, molecular mechanism that allows plants to coordinate physiological activities over 24-hour cycles called circadian rhythms. Photoperiodism is a collective term for the biological responses of plants to variations in the relative lengths of dark and light periods. The period of light-exposure is called the photoperiod.