Consider the forced damped oscillator equation y+9y Fsin(wt) For this forced oscillator to exhibi...
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2. Consider the undamped oscillator equation dy + 9y = cos(wt) dt2 y(0) = 0 v(0) = 0 What is the steady state frequency of this system? Use your solver to solve this ODE for w=4, w= 3.1, w = 3.01 and w 3. Comment on what the solutions look like as you change w. What happened with the last solution? I
Consider the following equation of motion for a damped driven harmonic oscillator: * + 1 + win = cos(wt) What is the general solution for this equation of motion (no derivation is required here) given that the oscillator is underdamped? Be sure to state which variables are your arbitrary constants.
4. A forced damped harmonic oscillator is modelled by the equation 6 dt2 dt 9ysin(2t) Perform an a-priory analysis, guessing what the behaviour of the solution should be. Find the solution y(t). Check the long term behaviour of our oscillator
4. A forced damped harmonic oscillator is modelled by the equation 6 dt2 dt 9ysin(2t) Perform an a-priory analysis, guessing what the behaviour of the solution should be. Find the solution y(t). Check the long term behaviour of our oscillator
Problem 15. (20 pts) Consider a damped driven oscillator with the following parameters s-100 N/m b=0.5kg/s m= 1 kg Fo=2N A) Find the resonant frequency, w. B) Find the damping rate y C) What is the quality factor Q for this oscillator? D) Is this oscillator lightly damped, critically damped, or heavily damped? E) Find the steady state amplitude when the oscillator is driven on resonance (Ω=w). F) Find the steady state amplitude when Ω_w+γ/2. G) Find the average power...
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Consider the equation for the forced oscillation of a damped system with hardening spring given by (cf. Problem 14.27). Solve this equation numerically in MatlabB with F( given by the step function excitation and ramp excitation, m 1, c= 0.5, k= 1, and μ= 0.01, 0.1, 1. Compare with the results obtained when μ-0.
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Consider the equation one gains from considering forced oscillations applied to a damped system d2y Fo -y= m c dy k cos(wt) dt2 m dt (a) Show that yp is a particular solution where, Fo - mw2) cos(wt) c sin(wt)). Yp(t) mw2)2 c2w2 - This can be written as Fo cos(wt - n), Ур (t) — where H and n are constants, independent of time. (b) Using this particular solution and the solution...
2. A damped harmonic oscillator with m 1.00 kg, k 2500 N/m, and b 42.4 kg/s is subject to a driving force given by Fo cos wt. (a) what value of ω results in the maximum stead-state amplitude (ie, resonance)? (b) What is the quality factor Q of this oscillator?
Q.3 Consider a damped harmonic oscillator. After four cycles the amplitude of the oscillator has dropped to 1/e of its initial value. Find the ratio of the frequency of the damped oscillator to its natural frequency.
4. Consider the differential equation y' - 6y' + 9y = 4e3t a) Find the general solution of the differential equation. b) Solve the IVP: Y" - 6y' +9y = 4e3with y(0) = 1 and y'(0) = 10.
Each of the following equation represents an unforced damped oscillator. Write the Laplace transform of the characteristic equation. And define if the system is over-damped, under-damped or critically damped. 1) 23 + 4 + 2x = 0 2) 3 +43 +3.2 = 0 3) 43 + 7 + 5x = 0 BIU A - A - IX E 33 x X, DE EV G* T 1 12pt Paragraph