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5. 20% Consider the base excitation problem for the configuration shown in the figure. In this...
solve the following question For the system shown in the figure below x and y denote,...
solve the following question
For the system shown in the figure below x and y denote, respectively, the absolute displacements of the mass m and the end Q of the damper c1 (1) Derive the equation of motion of the mass m (2) Find the steady state displacement of the mass m (3) Find the force transmitted to the support at P when the end Q is subjected to harmonic motion y (t)-y cos wt x(t) y(t) cos ω t
2(35%) Consider the system shown below. (a) Derive the equation of motion of the mass m. (b) Find the steady-state displacement of the mass m. (c) Find the force transmitted to the support at P...
2(35%) Consider the system shown below. (a) Derive the equation of motion of the mass m. (b) Find the steady-state displacement of the mass m. (c) Find the force transmitted to the support at P. y()-Ycos wt C2
2(35%) Consider the system shown below. (a) Derive the equation of motion of the mass m. (b) Find the steady-state displacement of the mass m. (c) Find the force transmitted to the support at P. y()-Ycos wt C2
3.26 For the base-excitation prototype shown in Figure 3.6, assume that the base dis- placement y()...
3.26 For the base-excitation prototype shown in Figure 3.6, assume that the base dis- placement y() is known, choose x(t) equation of motion by using Lagrange's equations. as the generalized coordinate, and derive the Package т тх Y k К(х — у) с(х — у) X о Base Figure 3.6. Base excitation and the free-body diagram of the mass -> 172
Use a plotting routine to examine the base motion problem (see Figure 2.13) by plotting the particular solution
Use a plotting routine to examine the base motion problem (see Figure 2.13) by plotting the particular solution (for an undamped system) for the three cases k = 1500 N/m, k = 2500 N/m, and k = 700 N/m. Also note the values of the three frequency ratios and the corresponding amplitude of vibration of each case compared to the input. Use the following values: 6) = 4.4 rad/s, m = 100 kg, and Y = 0.05 m.Figure 2.13 (a)...
5. Consider the periodie function of period T given by f(t) = (a) Sketch fo). (b) Expand ft) in a...
5. Consider the periodie function of period T given by f(t) = (a) Sketch fo). (b) Expand ft) in a Fourier series in the fornm 2rpt @pcos! ㅡ ㅡ l+, bnsin 2mpt p=1 (c) Derive the expression of the steady state response x() of a single degree-of-freedom (DOF) mass-spring-damper system subject to the excitation f(o).
5. Consider the periodie function of period T given by f(t) = (a) Sketch fo). (b) Expand ft) in a Fourier series in the fornm...
NOTE: this is base excitation not force vibration. 1: For the single degree of freedom system...
NOTE: this is base excitation not
force vibration.
1: For the single degree of freedom system driven by a harmonic base motion we discussed in the class. The governing equation is given by mž + ci + kx = cy + ky Where y(t) = Y sin wt and w is the driving (excitation) frequency. Given the initial conditions are x(0) = x, and (0) = v.. Combine the homogeneous and particular solutions and satisfy the initial conditions to obtain...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the...
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...
Question # 1: [25%] The system in the figure, m= 4 kg, a = 2 m,...
Question # 1: [25%] The system in the figure, m= 4 kg, a = 2 m, b= 3 m, k = 2500 N/m, c= 30 N.s/m, is subjected to a force excitation F(t)= F, sin(ot), where F = 1000 N. Find the maximum steady-state displacement of the mass for each of the following case: 1. The excitation frequency, o, is in the rage of 0-3 Hz. 2. The excitation frequency, o, is in the rage of 3-10 Hz 3. The...
Problem Statement 2: The "sky crane" shown on the text cover was a novel solution to...
Problem Statement 2: The "sky crane" shown on the text cover was a novel solution to the problem of landing the 2000 lb Curiosity rover on the surface of Mars. Curiosity hangs from the descent stage by 60-ft long nylon tethers (Figure 3a). The descent stage uses its thrusters to hover as the rover is lowered to the surface. Thus the rover behaves like a pendulum whose base is moving horizontally. The side thruster force is not constant but is...
The cart shown in Figure 3 is connected to the wall by spring kA. It weighs...
The cart shown in Figure 3 is connected to the wall by spring kA. It weighs 20 kgf and the system parameters are given as kA-800 N/m, kB = 600 N/m, CA-2 N sec/m, and g 9.81 m/sec2. The springs kA and kB are initially unstretched, and the mass m is at rest. For 0 < 3. K ta (t,-6n), the plate at the end of the spring-damper combination has motion defined by an Xp(t) = 25t mm. After t...
solve the following question
For the system shown in the figure below x and y denote, respectively, the absolute displacements of the mass m and the end Q of the damper c1 (1) Derive the equation of motion of the mass m (2) Find the steady state displacement of the mass m (3) Find the force transmitted to the support at P when the end Q is subjected to harmonic motion y (t)-y cos wt x(t) y(t) cos ω t
2(35%) Consider the system shown below. (a) Derive the equation of motion of the mass m. (b) Find the steady-state displacement of the mass m. (c) Find the force transmitted to the support at P. y()-Ycos wt C2
2(35%) Consider the system shown below. (a) Derive the equation of motion of the mass m. (b) Find the steady-state displacement of the mass m. (c) Find the force transmitted to the support at P. y()-Ycos wt C2
3.26 For the base-excitation prototype shown in Figure 3.6, assume that the base dis- placement y() is known, choose x(t) equation of motion by using Lagrange's equations. as the generalized coordinate, and derive the Package т тх Y k К(х — у) с(х — у) X о Base Figure 3.6. Base excitation and the free-body diagram of the mass -> 172
5. Consider the periodie function of period T given by f(t) = (a) Sketch fo). (b) Expand ft) in a Fourier series in the fornm 2rpt @pcos! ㅡ ㅡ l+, bnsin 2mpt p=1 (c) Derive the expression of the steady state response x() of a single degree-of-freedom (DOF) mass-spring-damper system subject to the excitation f(o).
5. Consider the periodie function of period T given by f(t) = (a) Sketch fo). (b) Expand ft) in a Fourier series in the fornm...
NOTE: this is base excitation not
force vibration.
1: For the single degree of freedom system driven by a harmonic base motion we discussed in the class. The governing equation is given by mž + ci + kx = cy + ky Where y(t) = Y sin wt and w is the driving (excitation) frequency. Given the initial conditions are x(0) = x, and (0) = v.. Combine the homogeneous and particular solutions and satisfy the initial conditions to obtain...
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...
Question # 1: [25%] The system in the figure, m= 4 kg, a = 2 m, b= 3 m, k = 2500 N/m, c= 30 N.s/m, is subjected to a force excitation F(t)= F, sin(ot), where F = 1000 N. Find the maximum steady-state displacement of the mass for each of the following case: 1. The excitation frequency, o, is in the rage of 0-3 Hz. 2. The excitation frequency, o, is in the rage of 3-10 Hz 3. The...
Problem Statement 2: The "sky crane" shown on the text cover was a novel solution to the problem of landing the 2000 lb Curiosity rover on the surface of Mars. Curiosity hangs from the descent stage by 60-ft long nylon tethers (Figure 3a). The descent stage uses its thrusters to hover as the rover is lowered to the surface. Thus the rover behaves like a pendulum whose base is moving horizontally. The side thruster force is not constant but is...
The cart shown in Figure 3 is connected to the wall by spring kA. It weighs 20 kgf and the system parameters are given as kA-800 N/m, kB = 600 N/m, CA-2 N sec/m, and g 9.81 m/sec2. The springs kA and kB are initially unstretched, and the mass m is at rest. For 0 < 3. K ta (t,-6n), the plate at the end of the spring-damper combination has motion defined by an Xp(t) = 25t mm. After t...
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