(normalized oscillator dynamics) consider a damped spring–mass system with dynamics mq¨+ cq˙ + kq = f. let ω0 = p k/m be the natural frequency and ζ = c/(2√km) be the damping ratio. a) show that by rescaling the equations, we can write the dynamics in the form q¨+ 2ζω0q˙ + ω2 0q = ω2 0u, (3.39) where u = f/k. this form of the dynamics is that of a linear oscillator with natural frequency ω0 and damping ratio ζ. b) show that the system can be further normalized and written in the form

explanation: in any substance/object, the particles inside it (atoms/molecules) constantly move in random directions and with random speeds (this motion is called brownian motion). as a result, the particles have some kinetic energy (which is proportional to the temperature of the substance).

explanation:

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unlike poles attract

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2

answer

procedural programming, object-oriented programming

explanation

procedural programming is a type of computer programming language that specifies a series of well structured steps and procedures   within its development period of time. it contains a systematic order of statements, functions and commands to complete a computational task or program. it is centered on creating procedures. while object oriented programming is a programming language that is centered on creating objects rather that actions and data rather than logic.. it has four principles which are inheritance, polymorphism, abstraction and encapsulation