oscillations - Sakshieducation.com
... position is x, the restoring force acting on it is F = -Kx If we displace the particle further through a small distance dx, then work done against the restoring force is given by dw = -Edx = +Kx dx The total work done in moving the SHO from mean position (x = 0) to displacement ‘x’ is given by ...
... position is x, the restoring force acting on it is F = -Kx If we displace the particle further through a small distance dx, then work done against the restoring force is given by dw = -Edx = +Kx dx The total work done in moving the SHO from mean position (x = 0) to displacement ‘x’ is given by ...
chapter 5
... Notes on the Moon’s Motion • We assumed the Moon orbits a “fixed” Earth • It is a good approximation • It ignores the Earth’s motion around the Sun • The Earth and Moon actually both orbit their center ...
... Notes on the Moon’s Motion • We assumed the Moon orbits a “fixed” Earth • It is a good approximation • It ignores the Earth’s motion around the Sun • The Earth and Moon actually both orbit their center ...
Powerpoint Slide
... When is the velocity maximum? V = - xMAX sin(t) velocity is max. when sin(t) is max (i.e. equals 1), this happens when (t) = /2 What are we doing today? 2 experiments. The first will allow us to measure the spring constant, k, of our spring. You will hang the spring, measure the equilibrium l ...
... When is the velocity maximum? V = - xMAX sin(t) velocity is max. when sin(t) is max (i.e. equals 1), this happens when (t) = /2 What are we doing today? 2 experiments. The first will allow us to measure the spring constant, k, of our spring. You will hang the spring, measure the equilibrium l ...
Chapter 2 Motion Along a Straight Line
... Suppose that to pump the gasoline, pay for it, and walk back to the truck takes you another 45 min. What is your average speed from the beginning of your drive to your return to the truck with the gasoline? ...
... Suppose that to pump the gasoline, pay for it, and walk back to the truck takes you another 45 min. What is your average speed from the beginning of your drive to your return to the truck with the gasoline? ...
Chapter 2 Motion Along a Straight Line
... Suppose that to pump the gasoline, pay for it, and walk back to the truck takes you another 45 min. What is your average speed from the beginning of your drive to your return to the truck with the gasoline? ...
... Suppose that to pump the gasoline, pay for it, and walk back to the truck takes you another 45 min. What is your average speed from the beginning of your drive to your return to the truck with the gasoline? ...
Brownian motion
Brownian motion or pedesis (from Greek: πήδησις /pˈɪːdiːsis/ ""leaping"") is the random motion of particles suspended in a fluid (a liquid or a gas) resulting from their collision with the quick atoms or molecules in the gas or liquid. Wiener Process refers to the mathematical model used to describe such Brownian Motion, which is often called a particle theoryThis transport phenomenon is named after the botanist Robert Brown. In 1827, while looking through a microscope at particles trapped in cavities inside pollen grains in water, he noted that the particles moved through the water but was not able to determine the mechanisms that caused this motion. Atoms and molecules had long been theorized as the constituents of matter, and many decades later, Albert Einstein published a paper in 1905 that explained in precise detail how the motion that Brown had observed was a result of the pollen being moved by individual water molecules. This explanation of Brownian motion served as definitive confirmation that atoms and molecules actually exist, and was further verified experimentally by Jean Perrin in 1908. Perrin was awarded the Nobel Prize in Physics in 1926 ""for his work on the discontinuous structure of matter"" (Einstein had received the award five years earlier ""for his services to theoretical physics"" with specific citation of different research). The direction of the force of atomic bombardment is constantly changing, and at different times the particle is hit more on one side than another, leading to the seemingly random nature of the motion.The mathematical model of Brownian motion has numerous real-world applications. For instance, Stock market fluctuations are often cited, although Benoit Mandelbrot rejected its applicability to stock price movements in part because these are discontinuous.Brownian motion is among the simplest of the continuous-time stochastic (or probabilistic) processes, and it is a limit of both simpler and more complicated stochastic processes (see random walk and Donsker's theorem). This universality is closely related to the universality of the normal distribution. In both cases, it is often mathematical convenience, rather than the accuracy of the models, that motivates their use.