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Respons6 0T 3) For a SDOF system with m-50kg and k 10000N/m) a. Determine the response for the pu...
1. A SDOF system with an equivalent mass of 20 kg, an equivalent stiffness of 3x10'...
1. A SDOF system with an equivalent mass of 20 kg, an equivalent stiffness of 3x10' N/m and an equivalent viscous damping coefficient of 2500 Ns/m. The system is subject to a sinusoidal pulse of pulse of magnitude 20000 N and total duration of 0.05 sec. Use the response spectrum for a sinusoidal pulse to determine the maximum displacement of the system.
Problem 3. The mass and stiffness of a SDOF system are 2 ks2/in. and 40 k...
Problem 3. The mass and stiffness of a SDOF system are 2 ks2/in. and 40 k /in., respectively. If the system is set into free vibration with the initial conditions u(0) = 0.7 in. and ů(0) = 5.6 in./s, derive expressions governing the displacement history for (a) c = 0 and (b) c = 2.8 k.s/in. Plot both responses on the same graph from t = 0 to 7 s at 0.01sec intervals. Determine the velocity of the system at...
Question 4 (25% total) Use the Duhamel Integral method to determine expression for the response x(t) of an undamped SDO...
Question 4 (25% total) Use the Duhamel Integral method to determine expression for the response x(t) of an undamped SDOF system to a rectangular pulse force F(t) as shown in Figure 4.1 F for O StSt Ffor («>) F(t) Fo Figure 4.1
Question 4 (25% total) Use the Duhamel Integral method to determine expression for the response x(t) of an undamped SDOF system to a rectangular pulse force F(t) as shown in Figure 4.1 F for O StSt Ffor («>)...
OUESTİON 2: (30 points) tp() Write the equation of motion for the SDOF system by taking the displ...
OUESTİON 2: (30 points) tp() Write the equation of motion for the SDOF system by taking the displacement coordinate to be the vertical displacement Z(t) at B. The system is rigid bar having uniformly distributed mass m 4 m 丯k Two concentrated masses m 2ma are located at B and C. The spring and damper are weightless. Assume that all displacements are small. Determine the natural period of the system.
OUESTİON 2: (30 points) tp() Write the equation of motion...
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...
The SDOF system in Fig. P4.10 is subjected to harmonic excitation z(f) = Z cos £2i applied at poi...
The SDOF system in Fig. P4.10 is subjected to harmonic excitation z(f) = Z cos £2i applied at point P. Express your answers to the following in terms of the givens: m, c, k, Z, and £2. (a) Derive the equation of motion of the system with the absolute displacement u(t) as the unknown, (b) Derive the equation of motion of the system with the relative displacement iv(t) = z — u as the unknown, (c) Determine expressions for co„...
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...
Problem 2 (25 points): Consider an undamped single-degree-of-freedom system with k = 10 N/m, 41 =...
Problem 2 (25 points): Consider an undamped single-degree-of-freedom system with k = 10 N/m, 41 = 10 N 92 = 8N, and m = 10 kg subjected to the harmonic force f(t) = qı sin(vt) + 92 cos(vt), v = 1 rad/ sec. Assume zero initial conditions (0) = 0 and c(0) = 0. Derive and plot the analytical solution of the displacement of the system. mm m = f(t) WWWWWWWW No friction Problem 2 Problem 3 (30 points): Using...
Question Four (a) Determine the response x() for the undamped system subjected to the force F...
Question Four (a) Determine the response x() for the undamped system subjected to the force F as shown below and given by: ts 0.1s F(t) =-600t +120 0.1 <t s 0.2 s t> 0.2s 600t 0 The mass is initially at rest with x 0 at time 1 0. (b) Find the displacement of the mass at 1 0.25 s. k 75 N/m 0.75 kg F), N 1, S 0.2 0.1
Question Four (a) Determine the response x() for the...
The system parameters of a freely-vibrating damped SDOF system are as follows: Mass, m= 100 kg...
The system parameters of a freely-vibrating damped SDOF system are as follows: Mass, m= 100 kg Damping Factor, c = 200 kg/s Spring Stiffness, k = 3000 N/m Initial Position, x, = 1 m Initial Velocity, v,= 0 m/s a) Create a MATLAB code and using the specified system parameters compute (using the correct units) the system characteristics: 1) natural (circular) frequency on; 2) cyclic frequency fn; 3) cyclic period p; 4) damped natural (circular) frequency 0g, and 5) damping...
1. A SDOF system with an equivalent mass of 20 kg, an equivalent stiffness of 3x10' N/m and an equivalent viscous damping coefficient of 2500 Ns/m. The system is subject to a sinusoidal pulse of pulse of magnitude 20000 N and total duration of 0.05 sec. Use the response spectrum for a sinusoidal pulse to determine the maximum displacement of the system.
Problem 3. The mass and stiffness of a SDOF system are 2 ks2/in. and 40 k /in., respectively. If the system is set into free vibration with the initial conditions u(0) = 0.7 in. and ů(0) = 5.6 in./s, derive expressions governing the displacement history for (a) c = 0 and (b) c = 2.8 k.s/in. Plot both responses on the same graph from t = 0 to 7 s at 0.01sec intervals. Determine the velocity of the system at...
Question 4 (25% total) Use the Duhamel Integral method to determine expression for the response x(t) of an undamped SDOF system to a rectangular pulse force F(t) as shown in Figure 4.1 F for O StSt Ffor («>) F(t) Fo Figure 4.1
Question 4 (25% total) Use the Duhamel Integral method to determine expression for the response x(t) of an undamped SDOF system to a rectangular pulse force F(t) as shown in Figure 4.1 F for O StSt Ffor («>)...
OUESTİON 2: (30 points) tp() Write the equation of motion for the SDOF system by taking the displacement coordinate to be the vertical displacement Z(t) at B. The system is rigid bar having uniformly distributed mass m 4 m 丯k Two concentrated masses m 2ma are located at B and C. The spring and damper are weightless. Assume that all displacements are small. Determine the natural period of the system.
OUESTİON 2: (30 points) tp() Write the equation of motion...
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...
Problem 2 (25 points): Consider an undamped single-degree-of-freedom system with k = 10 N/m, 41 = 10 N 92 = 8N, and m = 10 kg subjected to the harmonic force f(t) = qı sin(vt) + 92 cos(vt), v = 1 rad/ sec. Assume zero initial conditions (0) = 0 and c(0) = 0. Derive and plot the analytical solution of the displacement of the system. mm m = f(t) WWWWWWWW No friction Problem 2 Problem 3 (30 points): Using...
Question Four (a) Determine the response x() for the undamped system subjected to the force F as shown below and given by: ts 0.1s F(t) =-600t +120 0.1 <t s 0.2 s t> 0.2s 600t 0 The mass is initially at rest with x 0 at time 1 0. (b) Find the displacement of the mass at 1 0.25 s. k 75 N/m 0.75 kg F), N 1, S 0.2 0.1
Question Four (a) Determine the response x() for the...
The system parameters of a freely-vibrating damped SDOF system are as follows: Mass, m= 100 kg Damping Factor, c = 200 kg/s Spring Stiffness, k = 3000 N/m Initial Position, x, = 1 m Initial Velocity, v,= 0 m/s a) Create a MATLAB code and using the specified system parameters compute (using the correct units) the system characteristics: 1) natural (circular) frequency on; 2) cyclic frequency fn; 3) cyclic period p; 4) damped natural (circular) frequency 0g, and 5) damping...
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