The equation is- f=1/2π√g/L. Period (T) of a simple pendulum is T=2π√L/g. A simple pendulum consists of a mass (m) hanging from a string of length (L) and fixed at a pivot point (P). When it is displaced to an initial angle and then it is released, the pendulum ...
The Kundu–Mukherjee–Naskar equation (KMN) can model the data transmission in birefringent fibers through molecules or pulses in a few Femto-seconds. A fractional modification with Riemann-Liouville time-fractional derivative is suggested to take into account the discontinuous period, and the wave-...
In this paper we study the oscillatory behavior of a new class of memristor based neural networks with mixed delays and we prove the existence and uniqueness of the periodic solution of the system based on the concept of Filippov solutions of the differential equation with discontinuous right-hand...
Therefore, in Equation (2.3),Δτ can be the proper time between any two events. If the clock, and therefore the observer, is present at both events, the events must occur at the same spatial point for that observer. For example, to the captain of a spaceship who looks at the take-...
Equation (6) governs the evolution of \({\mathbf {y}}\) over an infinitesimally short period of time. Due to the Wiener processes, this evolution is inherently stochastic. Integrating the small changes in \({\mathbf {y}}\) over time, the state of the system can be expressed in functio...
A simple Pendulum consists of a point mass attached to a light inextensible string and suspended from a fixed support. Know the time period and energy of a simple pendulum with derivation.
The phonon Boltzmann transport equation (BTE) is a powerful tool for modeling and understanding micro-/nanoscale thermal transport in solids, where Fourier's law can fail due to non-diffusive effect when the characteristic length/time is comparable to the phonon mean free path/relaxation time. How...
Equation (11a) predicts that the temporal standard deviation for the first-passage time to threshold \(\Omega\) asymptotes to a constant value for \(\Omega \gtrsim 50\). Figure 3d confirms this prediction: the TSD is approximately the same for threshold optical densities 0.01–0.3 (correspondi...
In this phase, as we shall see, the density n displays oscillations over a period larger than that of the drive and up to a time that, thanks to the long-range interactions and despite the presence of multiple sources of noise, is exponentially large in the system size, a feature that ...
After an excitation by a laser beam, the fluorescence signal, If(t) , ideally decays exponentially according to the following equation where If(0) denotes the initial fluorescence intensity: (12)If(t)If(0)=exp(−t/τ) Lifetime measurements require only a single detection band and a ...