The damped harmonic oscillator systemsatisfies the equation mx + rx+ sx = 0.mž +rx +note: pay attention to the xThe displacement experienced by mass mcan be expressed by x = Ae^-rt/2m cos(w't+ Ø ). At t = 0, the mass is at x = x0velocity x (with one point) = v0. On thissystem it is known thatwi – w² = 10-6wž.a. If damping is removed, the mass willocillate in simple harmonic motion.Determine A and Ø in the parameters xo,vo and wo (the natural frequency of theoscillator).b. For this damped harmonic oscillator,determine A and Ø in the parameters xo,vo and w'.c. Calculate the logarithmic reduction9/11and quality factor Q.d. If w, = 10^6 rad/s and m = 10^-10kg,calculate the spring constant s and =coefficient r.

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The damped harmonic oscillator system satisfies the equation mx + rx+ sx = mx + rx + = 0. note: pay attention to the x The displacement experienced by mass m can be expressed by x = Ae^-rt/2m cos(w't + Ø ). At t = 0, the mass is at x = x0 velocity x (with one point) = v0. On this %3D system it is known that w3 – w'² = 10-°wž. a. If damping is removed, the mass will oscillate in simple harmonic motion. Determine A and Ø in the parameters xo, vo and wo (the natural frequency of the oscillator). b. For this damped harmonic oscillator, determine A and Ø in the parameters xo, vo and w'. c. Calculate the logarithmic reduction 9/11 and quality factor Q. d. If w, = 10^6 rad/s and m = 10^-10kg, calculate the spring constant s and = coefficient r.

The damped harmonic oscillator system satisfies the equation mx + rx+ sx = mx + rx + = 0. note: pay attention to the x The displacement experienced by mass m can be expressed by x = Ae^-rt/2m cos(w't + Ø ). At t = 0, the mass is at x = x0 velocity x (with one point) = v0. On this %3D system it is known that w3 – w'² = 10-°wž. a. If damping is removed, the mass will oscillate in simple harmonic motion. Determine A and Ø in the parameters xo, vo and wo (the natural frequency of the oscillator). b. For this damped harmonic oscillator, determine A and Ø in the parameters xo, vo and w'. c. Calculate the logarithmic reduction 9/11 and quality factor Q. d. If w, = 10^6 rad/s and m = 10^-10kg, calculate the spring constant s and = coefficient r.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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