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Consider the system below, write the equation of motion and calculate the response assuming that the...
Problem # 1 (b): Obtain a mathematical model of the system shown below. Problem1: Consider the ...
Problem # 1 (b): Obtain a mathematical model of the system shown below. Problem1: Consider the system shown below which is at rest for t<0. Assume the displacement x is the output of the system and is measured from the equilibrium position. Att-0, the cart is given initial conditions x(0)- xo and dx(0ydt v Obtain the output motion x0)Assume that m-10 kg, b-50 N-s/m, b-70 N-sm, -400 N/m, k2- 600 N/m. da diagam c.rditinstoo)20 추dx(Hat20.5m/s inilia) Problem12i Referring to Problem...
h 1 (25 Pts) Consider the system shown below C2. C1 ki k2 ky ka kı...
h 1 (25 Pts) Consider the system shown below C2. C1 ki k2 ky ka kı = 8 N/m, k,-100 N/m, k3-k,-50 N/m and c,-c2-16Ns/m. a) Determine the equation of motion for the system b) Compute the time constant and natural frequency of oscillation tain the free response for the initial conditions x(0)-1 and (0)-1
1 1 2 m2 1. Consider the system above. Derive the equation of motion and calculate the mass and s...
Please provide any MATLAB code you used for plotting.
1 1 2 m2 1. Consider the system above. Derive the equation of motion and calculate the mass and stiffness matrices. a) Calculate the characteristic equation forthe case m 9 kg m 1 kg k 24 N/m k2 3 N/mk3- 3 N/m and solve for the system's natural frequencies. b.) Calculate the eigenvectors u1 and u2 c.) Calculate xi(t) and x2(t), given x2(0)-1 mm, and xi(0) - vz(0) -vi(0) 0 d.)...
012) Write the equation of motion if the system is undamped as shown above and derive the displacement response of the...
012) Write the equation of motion if the system is undamped as shown above and derive the displacement response of the system if P(t) is given as in Figure 2. (4 Points) P(t) Po 2t Figure 2: P(t) force as a function of time
012) Write the equation of motion if the system is undamped as shown above and derive the displacement response of the system if P(t) is given as in Figure 2. (4 Points) P(t) Po 2t Figure...
Derive the equation of motion of the system below as a function of ki, k2, m,...
Derive the equation of motion of the system below as a function of ki, k2, m, 12, 13 and c. 2 k2 t Rigid Massless Link
consider the system shown where m=50kg, c=200N.s/m, k1=350N.m, and k2=550N.m. The free end of the spring...
consider the system shown where m=50kg, c=200N.s/m, k1=350N.m,
and k2=550N.m. The free end of the spring k2 is excited by
y(t)=0.4sin3t(m) as shown
4. Consider the system shown where m = 50 kg, c = 200 N.s/m, ki = 350 N.m, and k2 = 550 N.m. The free end of the spring ky is excited by y(t) = 0.4 sin 3t (m) as shown (20 points) a) Determine the equation of motion of the system. b) Determine the natural frequency...
For a spring-mass system, the mass is 4kg and stiffness 2500 N/m. Write the equation of...
For a spring-mass system, the mass is 4kg and stiffness 2500 N/m. Write the equation of response in the form of displacement using the following initial conditions: a) The mass is initially displaced by 100 mm from equilibrium position and released. b) The mass is struck by an impulse of 10 Ns, which acts along the direction of the mass.
mwu Q3. a) Consider the mechanical system shown, obtain the transfer function x(s)/P(s), assuming all initial...
mwu Q3. a) Consider the mechanical system shown, obtain the transfer function x(s)/P(s), assuming all initial conditions are zeros. (10 marks) Ž p3k, у b) For the question in part (a), assuming that m = 20 kg, b2 = 12 N.s/m, K1 = 20 N/m, K2 = 35 N/m and P=1 N. Write a MATLAB program to produce the response curve x(t). (15 Marks)
MEMB343 MECHANICAL VIBRATIONS ASSIGNMENT l. For the system shown in Figure 1, where mi=5 kg, m,-10 kg, ki=1000 N/m, k2-500 N/m, k, 2000 N/m, fi-100sin(15t) N and f-0, use modal analysis to determine...
MEMB343 MECHANICAL VIBRATIONS ASSIGNMENT l. For the system shown in Figure 1, where mi=5 kg, m,-10 kg, ki=1000 N/m, k2-500 N/m, k, 2000 N/m, fi-100sin(15t) N and f-0, use modal analysis to determine the amplitudes of masses m, and m2. The equations of motion are given as sin(15t), wth natura frequencies 5 01[i, 0 10 500-500x, 500 2500jx, x,[100 ω,-14.14 rad's and a, = 18.71 rad/s, and mode shapes, Φ',, and Φ' k, Im Figure 1
MEMB343 MECHANICAL VIBRATIONS ASSIGNMENT...
7. 150 points) A one-degree-of-freedom system is shown below. (a) (50 points) Derive the differential equation...
7. 150 points) A one-degree-of-freedom system is shown below. (a) (50 points) Derive the differential equation governing the motion of the system usingq, the (b) (25 points) what are the natural frequency and damping ratto of the system? c) (25 points) Mc)-0 (d) (25 points) (e) (25 points) If M(t) =1.2 sin m N clockwise angular displacement of the disk from equilibrium as the generalized coordinate. 10° and the system is given an initial angulan released from rest what is...
Problem # 1 (b): Obtain a mathematical model of the system shown below. Problem1: Consider the system shown below which is at rest for t<0. Assume the displacement x is the output of the system and is measured from the equilibrium position. Att-0, the cart is given initial conditions x(0)- xo and dx(0ydt v Obtain the output motion x0)Assume that m-10 kg, b-50 N-s/m, b-70 N-sm, -400 N/m, k2- 600 N/m. da diagam c.rditinstoo)20 추dx(Hat20.5m/s inilia) Problem12i Referring to Problem...
h 1 (25 Pts) Consider the system shown below C2. C1 ki k2 ky ka kı = 8 N/m, k,-100 N/m, k3-k,-50 N/m and c,-c2-16Ns/m. a) Determine the equation of motion for the system b) Compute the time constant and natural frequency of oscillation tain the free response for the initial conditions x(0)-1 and (0)-1
Please provide any MATLAB code you used for plotting.
1 1 2 m2 1. Consider the system above. Derive the equation of motion and calculate the mass and stiffness matrices. a) Calculate the characteristic equation forthe case m 9 kg m 1 kg k 24 N/m k2 3 N/mk3- 3 N/m and solve for the system's natural frequencies. b.) Calculate the eigenvectors u1 and u2 c.) Calculate xi(t) and x2(t), given x2(0)-1 mm, and xi(0) - vz(0) -vi(0) 0 d.)...
012) Write the equation of motion if the system is undamped as shown above and derive the displacement response of the system if P(t) is given as in Figure 2. (4 Points) P(t) Po 2t Figure 2: P(t) force as a function of time
012) Write the equation of motion if the system is undamped as shown above and derive the displacement response of the system if P(t) is given as in Figure 2. (4 Points) P(t) Po 2t Figure...
Derive the equation of motion of the system below as a function of ki, k2, m, 12, 13 and c. 2 k2 t Rigid Massless Link
consider the system shown where m=50kg, c=200N.s/m, k1=350N.m,
and k2=550N.m. The free end of the spring k2 is excited by
y(t)=0.4sin3t(m) as shown
4. Consider the system shown where m = 50 kg, c = 200 N.s/m, ki = 350 N.m, and k2 = 550 N.m. The free end of the spring ky is excited by y(t) = 0.4 sin 3t (m) as shown (20 points) a) Determine the equation of motion of the system. b) Determine the natural frequency...
mwu Q3. a) Consider the mechanical system shown, obtain the transfer function x(s)/P(s), assuming all initial conditions are zeros. (10 marks) Ž p3k, у b) For the question in part (a), assuming that m = 20 kg, b2 = 12 N.s/m, K1 = 20 N/m, K2 = 35 N/m and P=1 N. Write a MATLAB program to produce the response curve x(t). (15 Marks)
MEMB343 MECHANICAL VIBRATIONS ASSIGNMENT l. For the system shown in Figure 1, where mi=5 kg, m,-10 kg, ki=1000 N/m, k2-500 N/m, k, 2000 N/m, fi-100sin(15t) N and f-0, use modal analysis to determine the amplitudes of masses m, and m2. The equations of motion are given as sin(15t), wth natura frequencies 5 01[i, 0 10 500-500x, 500 2500jx, x,[100 ω,-14.14 rad's and a, = 18.71 rad/s, and mode shapes, Φ',, and Φ' k, Im Figure 1
MEMB343 MECHANICAL VIBRATIONS ASSIGNMENT...
7. 150 points) A one-degree-of-freedom system is shown below. (a) (50 points) Derive the differential equation governing the motion of the system usingq, the (b) (25 points) what are the natural frequency and damping ratto of the system? c) (25 points) Mc)-0 (d) (25 points) (e) (25 points) If M(t) =1.2 sin m N clockwise angular displacement of the disk from equilibrium as the generalized coordinate. 10° and the system is given an initial angulan released from rest what is...
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