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• Write the condition and an example for the resonance in a forced oscillation Show transcribed...
(1 point) This is an example of an Undamped Forced Oscillation where the phenomenon of Beats Occurs. Find the solution of the initial value problem: " +7.84z-5cos(3), (0) '(0) 0 Graph the solution to confirm the phenomenon of Beats. Note that you may have to use a large window in order to see more than one beat. What is the length of each beat? Length Would you be able to explain why the beats phenomenon occurs for this particular example?...
In the lecture note, the resonance of a forced oscillation is defined as a state where the amplitude of displacement reaches maximum. Resonance can also be defined for the acceleration, where the acceleration’s amplitude reaches maximum. (a) Find the frequency of acceleration resonance. (b) Assume the damping is very small, i.e. ? ≪ ?0, find the approximate expression of the frequency in (a) [Hint: using Taylor series] and compare it with the frequency of displacement resonance.
Q3 (40 p.) Find the oscillation frequency and oscillation condition for the circuit given below. * Based on your findings, fill the table. Your answer R HE C HE с R Osc. Freq. th R RB Osc. Cond.
Use Matlab and provide the code 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.
04: Let m = 2g, c = 0.08g/sec, and k = 20g/sec?, in a forced oscillation system under a non-sinusoidal periodic driving force, and f(t) = { t, -t, --1/2 <t</2 TI/2 < t <31/2 f(t) = f(t + 210) (15Marks) Find the steady-state solution?
5. (a) Express the loop gain of the following feedback system. (Spts) (b) What is the condition for the oscillation? (Spts) (c) Determine the oscillation frequency and R2 for the phase-shift oscillator C-0.1uF and R-1kohm. (5pts) R2 (vI) 5. (a) Express the loop gain of the following feedback system. (Spts) (b) What is the condition for the oscillation? (Spts) (c) Determine the oscillation frequency and R2 for the phase-shift oscillator C-0.1uF and R-1kohm. (5pts) R2 (vI)
determine how much resonance frequency is different from the natural oscillation frequency (1kHz) when the damping factor is 400/s
Question 3 An electromagnetic wave is coupled into a ring resonator. The resonance condition of the ring is that ma-nL, where m is an integer, λ is the wavelength, n is the refractive index of the medium and L is the geometrical length of the resonator path. a) If the resonator is made of glass, n = 1.46, and has a radius of 50pm, calculate the wavelengths of radiation that would meet the resonance condition for m =295 and m=296...
PROBLEM 5. TUNING A CIRCUIT: PRACTICAL RESONANCE. Consider a forced RLC circuit with L-1 (H), R-10 (12) and C 丽0 (f). Suppose an alternating current supplies a electromotive force Et)100 coswt. The equation modeling the charge Q(t) on the capacitor is 650 Q"(t) 10Q650Q(t) 100 coswt. a. Is the damping over-, under- or critical? Find the form of the general solution. Identify the transient and steady-state parts of the solution. b. Find the amplitude C(w) of the steady-state piece (here...
5. (Inhomogeneous equations: Laplace transforms: Resonance) A spring with spring constant k> 0 is attached to a m > 0 gram block. The spring starts from rest (x(0) - x'(0) 0 and is periodically forced with force f(t) - A sin(wft), with amplitude A > 0. (a) Write down the differential equation describing the displacement of the spring and the initial condition. (b) Solve the initial value problem from (a) using the Laplace transform. (c) What happens to the solution...