An excitation (Force) 60sin(ot)+80 cos(1) N produces a steady-state response (particular solution) whose quasi-static amplitude is...
Test Consider a two-degrees-of-freedom system shown below. ド. PN What is the amplitude of vibration (particular solution only) of mass 2 (at the input frequency)? The answer must be positive. Keep 3 significant figures, and omit units. Use m1 2 kg m2 4 kg k1 147 N/m k2 146 N/m K3 192 N/m F1 # 411 cos(0.50 N Note that the system is not damped. The homogeneous response does not decay to zero. The masses vibrates at three different frequencies...
Consider a single degree of freedom (SDOF) with mass-spring-damper system subjected to harmonic excitation having the following characteristics: Mass, m = 850 kg; stiffness, k = 80 kN/m; damping constant, c = 2000 N.s/m, forcing function amplitude, f0 = 5 N; forcing frequency, ωt = 30 rad/s. (a) Calculate the steady-state response of the system and state whether the system is underdamped, critically damped, or overdamped. (b) What happen to the steady-state response when the damping is increased to 18000 N.s/m? (Hint: Determine...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the system (state the concepts you use) (b) Write the characteristic equation of the system [4 marks 12 marks (c) What is the category of differential equations does the characteristic equation [2 marks fall into? (d) Prove that the steady state amplitude of vibration of the system is Xk Fo 25 + 0 marks (e) Prove that...
A 100 [kg] reciprocating internal combustion engine is fitted to a thin, massless beam using a vibrations damper. It is known that a machine with a rotating unbalance experiences a frequency squared harmonic excitation. The magnitude of the rotating unbalance is A = m,e = 0.3 [kg. m). 1. Calculate the nondimensional function for the state that has a steady state amplitude of 10 [mm] at a 90 [rad/s] speed. 2- Determine the frequency ratio, natural frequency, and the beams...
#40 a-f
B-A. (B+A ". Beats slation Recall the identity cos A-cos Be2-2A)sin(-2A) a. Show that 0-10,a, . 9 and (ii)o_10,us2toverify the identity. In which case do you see Gaph the functions on both sides of the equation in part (a) with (i) beats? b. 40 Analysis of the forced damped oscillation equation Consider the equation my"+ey'+ky Fo cos wof, which oscillator. Assume all the parameters in the equation are positive. a. Explain why the solutions of the homogeneous equation...
Please explain every step as clearly and detailed as
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B Frequency Response Modeling Frequency response modeling of a linear system is based on the premise that the dynamics of a linear system can be recovered from a knowledge of how the system responds to sinusoidal inputs. (This will be made mathematically precise in Theorem 13.) In other words, to determine (or iden- tify) a linear system, all one has to do is observe how the system reacts to sinusoidal...