PPT-N on-linear dynamics in damping rings

Yannis PAPAPHILIPPOU Accelerator and Beam Physics group Beams Department CERN Ninth International Accelerator School for Linear Colliders 26 October 6 November 2015 Whistler BC Canada. Response to Damping As we saw the unfor ced damped harmonic oscillator has equation 0 1 with 0 0 and 0 It has characteristic equation 2 0 with characteristic oots 2 2 Ther e ar e thr ee cases depending on the sign of the expr ession u N is the process noise or disturbance at time are IID with 0 is independent of with 0 Linear Quadratic Stochastic Control 52 brPage 3br Control policies statefeedback control 0 N called the control policy at time roughly speaking we choo Natural frequency and damping ratio Well consider the second order homogeneous linear constant coe57358 cient ODE bx cx with positive spring constantmass In the absence of damping term this spring constant wo 5 mm Half Dollar Money Clip CMCSDSP 38 mm Silver Dollar Money Clip Also available in Gold Filled brPage 7br Troy Findings 18002218014 brPage 8br Troy Findings 18002218014 Safety Pins brPage 9br Troy Findings 18002218014 Tie Tacks And Clutches brPage General . L. inear . B. eam Dynamics. S. Guiducci, INFN-LNF. Seventh International Accelerator School for Linear Colliders . Hosted by Raja . Ramanna. Centre for Advanced Technology. 4 December 2012. DRIVER VARIATIONS:The larger the driver the more import electrical damping is. Low frequency drivers andsubwoofers have the most problems regarding damping. Their moving mass is quite high andtheir su Typically, harmonic motion decreases in amplitude with time….this realistic model describes damped harmonic motion.. The damping effect is a result of friction and internal resistance of the system to further motion.. 1. Forced oscillator with damping. . resistance force is proportional to speed : . Equation of motion. 2. In ‘complex’ method. For convenience: . Also,. . k=m. w. 0. 2. 3. Solution of damped harmonic motion. Good Vibrations:. Standing waves can be produced on a string fixed at both ends if the length of the string . L. is a multiple of half the wavelength . l. ,. so that the ends of the string are nodes. These waves are called “harmonics” and are identified by “. . is a dissipation . of. . energy from a vibrating structure. .. The . term dissipate is used to . mean. . the transformation of . mechanical. . energy into other form of energy and, therefore, a removal . Describe . examples of damped oscillations.. . Need to know. - It is sufficient for students to know that damping involves a force that is always in the opposite direction to the direction of motion of the oscillating particle and that the force is a dissipative force.. Many pink diamond engagement rings are crafted using diamonds that vary in both color intensity and in secondary hue. Many pink diamond engagement rings that boast a secondary hue are still extremely beautiful and valuable and have a unique appeal all of their own. records . of the past, insights into the . future. Societal change. Tree rings and….. Water. Fire. Leonardo da Vinci (1500 AD). “Rings in the branches of sawed trees show the number of years and, . The five rings represent the five continents of the world. . The rings are five interlocking rings, . coloured. blue, yellow, black, green and red on a white field, known as the "Olympic rings". The symbol was originally created in 1913 by Coubertin. He appears to have intended the rings to represent the five continents: .