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4.62. Consider the following two-degree-of-freedom system and compute the response assuming modal damping ratios of (1...
1. Figure 1 plots a two-order system frequency response at five different damping ratios. The damping...
1. Figure 1 plots a two-order system frequency response at five different damping ratios. The damping ratios are 0.0.25, 0.5, 1.0, and 2.0, respectively. [5 marks] Output signal y(t) yo) - > (a) Identify the corresponding damping ratio of each curve (A1, A2, A3, A4, AS) tttt (b) If the natural frequency of this two-order system is 100 Hz and its damping ratio is A3, roughly estimate the response time for the system to reach the final stable state. tttttttt
A two degree of freedom system has a mass matrix, [M] and a non-normalized modal column...
A two degree of freedom system has a mass matrix, [M] and a non-normalized modal column matrix U given by 1 2 Find the normalized modal column matrix, U]n such that [U] [M][U]n-[ transpose and [4] is the identity matrix. I, where T' denotes the
1. Consider the two degree of freedom system shown. (a) Find the natural frequencies for the system (b) Determine the modal fraction for each mode. (c) Draw the mode shapes for each mode and iden...
1. Consider the two degree of freedom system shown. (a) Find the natural frequencies for the system (b) Determine the modal fraction for each mode. (c) Draw the mode shapes for each mode and identify any nodes for each mode. (d) Demonstrate mode shape orthogonality. (e) If F- and the motion is initiated by giving the mass whose displacement is a velocity of 0.2 m/s when in equilibrium, determine 0) and ,0 (f) Determine the steady-state solution for both *)...
Consider a single degree of freedom (SDOF) with mass-spring-damper system
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...
solve by matlab The damping system has a single degree of freedom as follows: dx2 dx...
solve by matlab
The damping system has a single degree of freedom as follows: dx2 dx mo++ kx = F(t) dt dt The second ordinary differential equation can be divided to two 1sorder differential equation as: dx dx F C k xí -X2 -X1 dt dt m m m = x2 ,x'z m N F = 10, m = 5 kg k = 40, and the damping constant = 0.1 The initial conditions are [00] and the time interval is...
using matlab The damping system has a single degree of freedom as follows: dx2 dx m++...
using matlab
The damping system has a single degree of freedom as follows: dx2 dx m++ kx = + kx = F(t) dt dt The second ordinary differential equation can be divided to two 1st order differential equation as: dx dx F с k x1 = = x2 ,X'2 X2 -X1 dt dt m m m m N F = 10, m = 5 kg k = 40, and the damping constant = 0.1 The initial conditions are [0 0]...
13. Briefly describe how a two degree of freedom system can be made to vibrate in one of its pure...
13. Briefly describe how a two degree of freedom system can be made to vibrate in one of its pure modes. sャ 2. (a) Sketch the amplitude ratio and phase angle for damping of 0.01 and 0.3, and indicate the peak amplitude values. Name the axes with correct numerica (b) Compare this amplitude diagram with a similar one that corresponds to base excitation, emphasizing t a single degree of freedom system subjected to harmonic force with phasizing the differences (15)...
path Wordsso QUESTION 7 A single degree of freedom system is excited by a harmonic force...
path Wordsso QUESTION 7 A single degree of freedom system is excited by a harmonic force with amplitude 167 N at the frequency ratio 0.9. The amplitude of response is measured as 0.05 m. If the equivalent stiffness of the system is 12 kN/m, calculate the damping ratio of this system. Give your answer with 3 digits after the decimal point. Click Save and submit to save and submit. Click Save answers to save all answers e 9 0 *...
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping...
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping c and spring stiffness k: a.- Show that the particular solution for the equation with an applied force fo cos(ot), i.e., Mä+ci+kx=f, cos(or) can be expressed as x )= A cos(ot) + A, sin(or) and find the values of A, and A, that solve the differential equation in terms of M, c, k and fo. 5 points. b. Use the result from part a...
[1] 25 pts. A damped single degree of freedom system without applied forces is oscillating due to...
solve for #2
[1] 25 pts. A damped single degree of freedom system without applied forces is oscillating due to a certain unknown initial conditions. Derive a response equation x(t) for the following four cases. a. 5 pts. 0 (no damping) b. 10 pts. 0<1 (underdamped) c. 5 pts. >1 (overdamped) d. 5 pts. ๕-1 (critically damped) Here the is the damping ratio of the oscillating system. [2] 5 pts. For the same system of underdamped case with initial conditions...
1. Figure 1 plots a two-order system frequency response at five different damping ratios. The damping ratios are 0.0.25, 0.5, 1.0, and 2.0, respectively. [5 marks] Output signal y(t) yo) - > (a) Identify the corresponding damping ratio of each curve (A1, A2, A3, A4, AS) tttt (b) If the natural frequency of this two-order system is 100 Hz and its damping ratio is A3, roughly estimate the response time for the system to reach the final stable state. tttttttt
A two degree of freedom system has a mass matrix, [M] and a non-normalized modal column matrix U given by 1 2 Find the normalized modal column matrix, U]n such that [U] [M][U]n-[ transpose and [4] is the identity matrix. I, where T' denotes the
1. Consider the two degree of freedom system shown. (a) Find the natural frequencies for the system (b) Determine the modal fraction for each mode. (c) Draw the mode shapes for each mode and identify any nodes for each mode. (d) Demonstrate mode shape orthogonality. (e) If F- and the motion is initiated by giving the mass whose displacement is a velocity of 0.2 m/s when in equilibrium, determine 0) and ,0 (f) Determine the steady-state solution for both *)...
solve by matlab
The damping system has a single degree of freedom as follows: dx2 dx mo++ kx = F(t) dt dt The second ordinary differential equation can be divided to two 1sorder differential equation as: dx dx F C k xí -X2 -X1 dt dt m m m = x2 ,x'z m N F = 10, m = 5 kg k = 40, and the damping constant = 0.1 The initial conditions are [00] and the time interval is...
using matlab
The damping system has a single degree of freedom as follows: dx2 dx m++ kx = + kx = F(t) dt dt The second ordinary differential equation can be divided to two 1st order differential equation as: dx dx F с k x1 = = x2 ,X'2 X2 -X1 dt dt m m m m N F = 10, m = 5 kg k = 40, and the damping constant = 0.1 The initial conditions are [0 0]...
13. Briefly describe how a two degree of freedom system can be made to vibrate in one of its pure modes. sャ 2. (a) Sketch the amplitude ratio and phase angle for damping of 0.01 and 0.3, and indicate the peak amplitude values. Name the axes with correct numerica (b) Compare this amplitude diagram with a similar one that corresponds to base excitation, emphasizing t a single degree of freedom system subjected to harmonic force with phasizing the differences (15)...
path Wordsso QUESTION 7 A single degree of freedom system is excited by a harmonic force with amplitude 167 N at the frequency ratio 0.9. The amplitude of response is measured as 0.05 m. If the equivalent stiffness of the system is 12 kN/m, calculate the damping ratio of this system. Give your answer with 3 digits after the decimal point. Click Save and submit to save and submit. Click Save answers to save all answers e 9 0 *...
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping c and spring stiffness k: a.- Show that the particular solution for the equation with an applied force fo cos(ot), i.e., Mä+ci+kx=f, cos(or) can be expressed as x )= A cos(ot) + A, sin(or) and find the values of A, and A, that solve the differential equation in terms of M, c, k and fo. 5 points. b. Use the result from part a...
solve for #2
[1] 25 pts. A damped single degree of freedom system without applied forces is oscillating due to a certain unknown initial conditions. Derive a response equation x(t) for the following four cases. a. 5 pts. 0 (no damping) b. 10 pts. 0<1 (underdamped) c. 5 pts. >1 (overdamped) d. 5 pts. ๕-1 (critically damped) Here the is the damping ratio of the oscillating system. [2] 5 pts. For the same system of underdamped case with initial conditions...
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