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3) Consider the following vibrating system u" (1/4) 2u 2 cos (wt), u (0) 0, (0) 2 (a) Find transient and steady states of solution (b) Find the amplitude R of the steady state solution in terms o...
Consider a damped forced mass-spring system with m = 1, γ = 2, and k =...
Consider a damped forced mass-spring system with m = 1, γ = 2, and k = 26, under the influence of an external force F(t) = 82 cos(4t). a) (8 points) Find the position u(t) of the mass at any time t, if u(0) = 6 and u 0 (0) = 0. b) (4 points) Find the transient solution uc(t) and the steady state solution U(t). How would you characterize these two solutions in terms of their behavior in time?...
3. Consider the forced but undamped system described by the initial value problem u" +u =...
3. Consider the forced but undamped system described by the initial value problem u" +u = 3 cos(wt), 4(0) = 0, 1'0) = 0. a. Find solution for u(t) when w 1. b. Plot the solution u(t) versus t for w = 0.7, 0.8, and 0.9. Describe how the response u(t) changes as w varies. What happens when w gets close to 1? Note that the natural frequency of the system is wo = 1.
dy dy dx2 dx tycos(ox 8) Solve: 47+d7+y - cos(ox) Find the amplitude of the steady-state solution (after transients have died down) in terms of w. The find the value of that makes the amplitude as...
dy dy dx2 dx tycos(ox 8) Solve: 47+d7+y - cos(ox) Find the amplitude of the steady-state solution (after transients have died down) in terms of w. The find the value of that makes the amplitude as large as possible.
dy dy dx2 dx tycos(ox 8) Solve: 47+d7+y - cos(ox) Find the amplitude of the steady-state solution (after transients have died down) in terms of w. The find the value of that makes the amplitude as large as possible.
7. Identify the transient and steady state components of the following system responses. Do not just...
7. Identify the transient and steady state components of the following system responses. Do not just underline the portions of the problem statement. Write your answers as as Is(t) = and Xtr(t) = (a) r(t) = A cos(wit) + (1+e-B) sin(wyt) + Du(t), B > 0 (b) r(t) = e-C+ [A + Bt] + D [1 - e-F!(P+Qt) + cos(wt)],C > 0,F > 0 Page 4 (c) r(t) = 1 + e- cos(t) +e-24 + sin(t)
help with matlab 2. Consider the undamped oscillator equation dy + 9y = cos(wt) dt2 y(0)...
help with matlab
2. Consider the undamped oscillator equation dy + 9y = cos(wt) dt2 y(0) = 0 v(0) = 0 What is the steady state frequency of this system? Use your solver to solve this ODE for w=4, w= 3.1, w = 3.01 and w 3. Comment on what the solutions look like as you change w. What happened with the last solution? I
please find amplitude and freq of the steady state solution An 8-kg mass is attached to...
please find amplitude and freq
of the steady state solution
An 8-kg mass is attached to a spring hanging from the ceiling and allowed to come to rest. Assume that the spring constant is 20 N/m and the damping constant is 2 N-sec/m. At time t= 0, an external force of 4 sin 2t cos 2t is applied to the system. Determine the amplitude and frequency of the steady-state solution.
damped forced mass-spring system with m 2, and k 26, under the 2 Consider a influence...
damped forced mass-spring system with m 2, and k 26, under the 2 Consider a influence of an external force F(t)= 82 cos (4t) 1, 7 = a) (8 points) Find the position u(t) of the mass at any time t, if u(0) 6 and u'(0) = 0. b) (4 points) Find the transient solution u(t) and the steady state solution U(t). How would you characterize these two solutions in terms of their behavior in time? We were unable to...
2. Find the steady-state temperature u(r,0) in a semicircular plate of radius r 2 if [10<0<...
2. Find the steady-state temperature u(r,0) in a semicircular plate of radius r 2 if [10<0< π/2 u(2,0) and the edges 0 = 0 and 0 = T are insulated. 0 /20 T пл sin 2 1 2 + cos(n0) Ans: u(r,0) п
Problem 7 If A cos 0,+B sin oft = rsin(0 -0) = R cos(t-8), (a) determiner...
Problem 7 If A cos 0,+B sin oft = rsin(0 -0) = R cos(t-8), (a) determiner and in terms of A and B , and (b) the relationship among R,r, 8 and 2 Ans. (a) r = VA’ + Bº, tan 0 4 b)r=R, 0 = 8-5, tan tan 8 +1 = 0 Problem 8 (a) Define the steady state solution of a given SLDE. (b) Consider the motion of a 2-kg mass in a (m,c,k)-system under a cyclic load....
4 Consider the system represented in state variable form 0 x+ 2 y [1-1x +[0]u B...
4 Consider the system represented in state variable form 0 x+ 2 y [1-1x +[0]u B C(sl- A) Show that a transfer function is related to the state equation by H(s) a) D, and find the transfer function for the system above. (5 marks) Sketch the Bode plot. b) (5 marks)
4 Consider the system represented in state variable form 0 x+ 2 y [1-1x +[0]u B C(sl- A) Show that a transfer function is related to the state equation...
3. Consider the forced but undamped system described by the initial value problem u" +u = 3 cos(wt), 4(0) = 0, 1'0) = 0. a. Find solution for u(t) when w 1. b. Plot the solution u(t) versus t for w = 0.7, 0.8, and 0.9. Describe how the response u(t) changes as w varies. What happens when w gets close to 1? Note that the natural frequency of the system is wo = 1.
dy dy dx2 dx tycos(ox 8) Solve: 47+d7+y - cos(ox) Find the amplitude of the steady-state solution (after transients have died down) in terms of w. The find the value of that makes the amplitude as large as possible.
dy dy dx2 dx tycos(ox 8) Solve: 47+d7+y - cos(ox) Find the amplitude of the steady-state solution (after transients have died down) in terms of w. The find the value of that makes the amplitude as large as possible.
7. Identify the transient and steady state components of the following system responses. Do not just underline the portions of the problem statement. Write your answers as as Is(t) = and Xtr(t) = (a) r(t) = A cos(wit) + (1+e-B) sin(wyt) + Du(t), B > 0 (b) r(t) = e-C+ [A + Bt] + D [1 - e-F!(P+Qt) + cos(wt)],C > 0,F > 0 Page 4 (c) r(t) = 1 + e- cos(t) +e-24 + sin(t)
help with matlab
2. Consider the undamped oscillator equation dy + 9y = cos(wt) dt2 y(0) = 0 v(0) = 0 What is the steady state frequency of this system? Use your solver to solve this ODE for w=4, w= 3.1, w = 3.01 and w 3. Comment on what the solutions look like as you change w. What happened with the last solution? I
please find amplitude and freq
of the steady state solution
An 8-kg mass is attached to a spring hanging from the ceiling and allowed to come to rest. Assume that the spring constant is 20 N/m and the damping constant is 2 N-sec/m. At time t= 0, an external force of 4 sin 2t cos 2t is applied to the system. Determine the amplitude and frequency of the steady-state solution.
damped forced mass-spring system with m 2, and k 26, under the 2 Consider a influence of an external force F(t)= 82 cos (4t) 1, 7 = a) (8 points) Find the position u(t) of the mass at any time t, if u(0) 6 and u'(0) = 0. b) (4 points) Find the transient solution u(t) and the steady state solution U(t). How would you characterize these two solutions in terms of their behavior in time? We were unable to...
2. Find the steady-state temperature u(r,0) in a semicircular plate of radius r 2 if [10<0< π/2 u(2,0) and the edges 0 = 0 and 0 = T are insulated. 0 /20 T пл sin 2 1 2 + cos(n0) Ans: u(r,0) п
Problem 7 If A cos 0,+B sin oft = rsin(0 -0) = R cos(t-8), (a) determiner and in terms of A and B , and (b) the relationship among R,r, 8 and 2 Ans. (a) r = VA’ + Bº, tan 0 4 b)r=R, 0 = 8-5, tan tan 8 +1 = 0 Problem 8 (a) Define the steady state solution of a given SLDE. (b) Consider the motion of a 2-kg mass in a (m,c,k)-system under a cyclic load....
4 Consider the system represented in state variable form 0 x+ 2 y [1-1x +[0]u B C(sl- A) Show that a transfer function is related to the state equation by H(s) a) D, and find the transfer function for the system above. (5 marks) Sketch the Bode plot. b) (5 marks)
4 Consider the system represented in state variable form 0 x+ 2 y [1-1x +[0]u B C(sl- A) Show that a transfer function is related to the state equation...
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