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2. (25%) Consider an undamped system subject to a rectangular pulse given by F(t) Fo for...
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 («>)...
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...
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...
Consider an undamped system where the vector-matrix form of the system model is: [F(t) [8 orë...
Consider an undamped system where the vector-matrix form of the system model is: [F(t) [8 orë Mx + x = LO 183, 2000 -1800 x (-1800 45001 The system is initially at rest with X (0) = 0 and 2,0)=0 when input F(t) = 84 sin 15t is applied to the system. Use the modal decomposition method described in chapter 5 to find the system response. Some intermediate results (find these as part of your solution) are: The system's two...
Consider an undamped system where the vector-matrix form of the system model is: F(t) [8 olx...
Consider an undamped system where the vector-matrix form of the system model is: F(t) [8 olx Mx + Kx = 0 18X, + 2000 -1800 x -1800 4500 I:1-[0] The system is initially at rest with x(0) = 0 and x,0)=0 when input F(t) = 84 sin15t is applied to the system. Use the modal decomposition method described in chapter 5 to find the system response. Some intermediate results (find these as part of your solution) are: The system's two...
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...
Consider an undamped system where the vector-matrix form of the system model is: [F(t) [18 07ž...
Consider an undamped system where the vector-matrix form of the system model is: [F(t) [18 07ž Mx + Kx = 083, + [18000 -72007x -7200 8000X, E]-[] The input to the system is F(t) = 6300 sin (30t). Use modal decomposition to find the system's frequency response. Note that the frequency response is the particular solution, and also called the steady-state response.
State vIIU F(0) 3) (25 pts.) Find the response of an undamped single degree of freedom systerm to the excitation F(t...
State vIIU F(0) 3) (25 pts.) Find the response of an undamped single degree of freedom systerm to the excitation F(t) shown on the right using the convolution integral. cos 21 to
State vIIU F(0) 3) (25 pts.) Find the response of an undamped single degree of freedom systerm to the excitation F(t) shown on the right using the convolution integral. cos 21 to
s (t) is a rectangular pulse given by, s(t) 0, elsewhere. A matched filter which is...
s (t) is a rectangular pulse given by, s(t) 0, elsewhere. A matched filter which is matched to s(t) has unit pulse response h( The input to the matched filter is x(t), which is given by x (t) s(t) +n(t), where n(t) is zero mean white Gaussian noise with power spocial density of Tho maichod filier ouipu is y (i) What is h(t), as a function of A and T? What is H(f), the Fourier Tranform of h (t)? What...
Consider the square pulse f(t) shown in the figure below. If we compress the pulse by a factor c ...
Consider the square pulse f(t) shown in the figure below. If we
compress the pulse by a factor c > 1 and at the same time
amplify its amplitude by the same factor c, we get a new function
g(t) as shown in the figure (c = 2 for the given figure).
Q.6. Consider the square pulse f(t) shown in the figure below. If we compress the pulse by a factor c>1 and at the same time amplify its amplitude...
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 («>)...
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...
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...
Consider an undamped system where the vector-matrix form of the system model is: [F(t) [8 orë Mx + x = LO 183, 2000 -1800 x (-1800 45001 The system is initially at rest with X (0) = 0 and 2,0)=0 when input F(t) = 84 sin 15t is applied to the system. Use the modal decomposition method described in chapter 5 to find the system response. Some intermediate results (find these as part of your solution) are: The system's two...
Consider an undamped system where the vector-matrix form of the system model is: F(t) [8 olx Mx + Kx = 0 18X, + 2000 -1800 x -1800 4500 I:1-[0] The system is initially at rest with x(0) = 0 and x,0)=0 when input F(t) = 84 sin15t is applied to the system. Use the modal decomposition method described in chapter 5 to find the system response. Some intermediate results (find these as part of your solution) are: The system's two...
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...
Consider an undamped system where the vector-matrix form of the system model is: [F(t) [18 07ž Mx + Kx = 083, + [18000 -72007x -7200 8000X, E]-[] The input to the system is F(t) = 6300 sin (30t). Use modal decomposition to find the system's frequency response. Note that the frequency response is the particular solution, and also called the steady-state response.
State vIIU F(0) 3) (25 pts.) Find the response of an undamped single degree of freedom systerm to the excitation F(t) shown on the right using the convolution integral. cos 21 to
State vIIU F(0) 3) (25 pts.) Find the response of an undamped single degree of freedom systerm to the excitation F(t) shown on the right using the convolution integral. cos 21 to
s (t) is a rectangular pulse given by, s(t) 0, elsewhere. A matched filter which is matched to s(t) has unit pulse response h( The input to the matched filter is x(t), which is given by x (t) s(t) +n(t), where n(t) is zero mean white Gaussian noise with power spocial density of Tho maichod filier ouipu is y (i) What is h(t), as a function of A and T? What is H(f), the Fourier Tranform of h (t)? What...
Consider the square pulse f(t) shown in the figure below. If we
compress the pulse by a factor c > 1 and at the same time
amplify its amplitude by the same factor c, we get a new function
g(t) as shown in the figure (c = 2 for the given figure).
Q.6. Consider the square pulse f(t) shown in the figure below. If we compress the pulse by a factor c>1 and at the same time amplify its amplitude...
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