Forced oscillators and damping in textbook "Classical Mechanics: A Modern Perspective" by Vernon Barger and Martin Olsson.
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- A one-dimensional mass-on-a-spring oscillator is damped by a damping force proportional to the velocity of the mass. Show explicitly that the time rate of decrease of the total energy is equal to minus the powerdissipated by the damping force. b)If the oscillator is critically damped, show that it can never pass through the equilibrium position more than once.c)If the oscillator is overdamped, show that it can never pass through the equilibrium position more than onceConsider a which m" ů O•os hq and 'k is 5ONm. State and sketch the nature f oscillatog. motion when the damping Constant b is )0.1N - s/m li) L-ON-5/m and SN-5/m. damped hamardk osallator derdamped harmanic oscillator, haS damping constant a = 2 We, that is acted upon by a driving force F = Fo sin wt, The system Starts from rest With an and initial displacement of Xo lie,xLO) = Xo 10)=0), Find the equation of motion and its corres panding salution xlt), determine all of the coefficients le.g., Ai,A2, B,, Bzretc) %3D Be,Bz,et c)
- A spring mass system consists of a sping with spring constant k and an attached block of mass m is submerged in a liquid that produces a damping force Fr. m=2kg Fr= 18 times the instaneous velocity of the center of mass of the block k=36 n/m If the mass is initially released from rest 1 meter below equilibrium position a. Give a 2nd degree equation that describe the motion of the center of mass of the attached block b. Solve the equation in part ayou have a spring. you stick a ball with a mass of 3 killograms on it. you know the damping constant is 6. the spring with the mass on it can be extended 2.5 m beond its equlibrium length when a force of 5 newtons acts on it. assume that you stetch the spring to 5 meters beond its natural equilibrium length and then you realse it with zero velocity. in the notation of the text, what is the value c2-4mk? write your answer in the blank provided below: ______________________m2kg2/sec2