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Coriolis Flowmeters
Published in Jesse Yoder, New-Technology Flowmeters, 2023
We are about to stare into the soul of a Coriolis flowmeter, so let's make sure we understand the terms. First, we say the tube oscillates, or if there are two, the tubes oscillate. This means they go back and forth. Oscillation is a to and fro motion, like a pendulum. It is not rotation; it is oscillation. As explained earlier, the Coriolis tubes are made to oscillate by an electromagnetic exciter.
Units and Measurements
Published in Daniel H. Nichols, Physics for Technology, 2019
Pendulum: A pendulum could be simply a weight on a string swinging back and forth, repeating its motion at a regular rate. A repetitive motion is known as an oscillation. One back-and-forth motion is one oscillation. To time something with a pendulum, simply count the number of complete back-and-forth motions or oscillations during any action being timed and multiply this number by the time for one oscillation of the pendulum (Figure 1.27).
Applications of the Formalism-II
Published in Shabnam Siddiqui, Quantum Mechanics, 2018
A harmonic oscillator is a system that exhibits simple harmonic motion or periodic motion, a motion that repeats itself after equal intervals of time. Such a motion is caused by a restoring force, which is proportional to displacement of the oscillator and acts in a direction opposite to the displacement. Many systems such as spring, simple pendulum, vibrating string and molecular vibration can be approximated as simple harmonic oscillators. In classical physics, such systems are well understood. Therefore, the most natural question to ask is, what is a quantum mechanical simple harmonic motion? What are its properties? Its study is key to understanding the vibration of individual atoms in molecules and crystals. It is also very important for understanding particle properties of an electromagnetic wave. In this chapter, first we solve the Schrodinger equation for a harmonic oscillator using two methods, analytical method and algebraic method. Later, we discuss the quantum properties of the harmonic oscillator.
Applications of Elzaki decomposition method to fractional relaxation-oscillation and fractional biological population equations
Published in Applied Mathematics in Science and Engineering, 2023
Lata Chanchlani, Mohini Agrawal, Rupakshi Mishra Pandey, Sunil Dutt Purohit, D. L. Suthar
In physical, chemical and biological processes, an oscillator is something that exhibits a rhythmic periodic reaction. Many real mechanical, radio-technical, biological and other things have oscillatory processes in which a slow smooth transition of an object’s status over a finite length of time shifts to an irregular change of status over an incredibly short period. The behaviour of a physical system returning to equilibrium after being disrupted provides the basis for a relaxation oscillation. A damped oscillating system is an oscillator that fades away over time owing to energy loss, such as a swinging pendulum, a weight on a spring or a resistor-inductor-capacitor circuit. Relaxation and damped oscillations are described by ordinary differential equations of order one and two, respectively.
Computational modelling in sport: a hybrid simulation of the runner as a complex adaptive system
Published in Theoretical Issues in Ergonomics Science, 2022
E. Vermeulen, S. S. Grobbelaar, A. Botha, K. Nolte
A mathematical expression is required to provide the computational steps in the simulation model with a quantified value for the training load. The training load is quantified in a mathematical expression that connects the elements of the runner in a composite value to represent the perturbation of homeostasis through cyclical impact loading. The derivation of the impact loading takes inspiration from the established concept of the runner as a spring-mass system (Farley and González 1996; Ferris and Farley 1997; Morin 2018; Girard et al. 2013; Moore 2016; Kulmala et al. 2018). The runner may be represented as a linear spring-mass system consisting of a single mass (the body) that oscillates around an equilibrium position (defined as where the vertical ground reaction force equals body weight, (Cavagna, Legramandi, and Peyré-Tartaruga 2008)) with the legs acting as springs. The repetitive up-and-down movement of the center of mass of a runner represents a wave-form function over time (Clark, Ryan, and Weyand 2017), and can be modelled as simple harmonic motion. In simple harmonic motion the displacement, velocity, and acceleration of an oscillating object is modelled as sinusoidal functions of time.
Surge and heave hydrodynamic coefficients for a combination of a porous and a rigid cylinder in motion in finite ocean depth
Published in Waves in Random and Complex Media, 2021
Abhijit Sarkar, Swaroop Nandan Bora
Solving radiation problems for ocean waves yields the important hydrodynamic coefficients, namely, added mass and damping coefficients. These coefficients arise as the real and imaginary parts of the hydrodynamic reaction loads on the body due to the prescribed body motions. In physical sense, the added mass is the weight added to a system in a fluid due to the fact that an accelerating or decelerating body must move some volume of surrounding fluid with it as it moves. Damping is an influence within or upon an oscillatory system that has the effect of reducing, restricting or preventing its oscillations. The hydrodynamic forces in the x- and z-directions (i.e. for surge and heave motions) due to the motion of the cylinder in modes m = 1, 2 can be found out by integrating the corresponding pressure over the cylinder. For this configuration, only surge motion is considered. The following explains why heave motion is not considered for this problem: