mint88
2010-10-26, 22:58
老师布置的作业
matlab以前跟着老师一步一步做过
但是现在完全不会T T
各位大神帮我看一下吧
5. in this problem, we’ll investigate the effect of damping on the pendulum, using the model:
Theta” + b*theta’ + sin(theta) = 0
Prepare simulink models that will take the value of b from a “Constant” block and
Plot the numerical solution of this differential equation with initial conditions theta(0) = 0, theta’(0) = 4, from t = 0 to t = 20.
Do the same for linear approximation:
Theta” + b*theta’ + theta = 0
Compare the linear and nonlinear behavior for the values b = 1, 1.5, and 2. Interpret what is happening physically in each case; i.e., describe explicitly what the graph says the pendulum is doing.
6. in this problem we’ll look at the effect of a periodic external force on the pendulum, using the model
Theta” + 0.05*theta’ + sin(theta) = 0.3 cos wt (*)
We have chosen a value for the damping coefficient that is more typical of air resistance than the values in the previous problem. Prepare simulink models for (*) and its linear appoximation:
Theta” + 0.05*theta’ + theta = 0.3 cos wt
The right hand side can be produced by a sine wave block (which is in the sourses library). When you install this block and left click on it to bringup the block parameters menu, you will see an amplitude box in which to insert the parameter 0.3 and a frequency box in which to insert the parameter w. note that since we have a cosine, not a sine, you also have to adjust the Phase (to pi/2, since cos wt = sin (wt + pi/2)).
Plot the numerical solution of this differential equation with initial conditions theta(0) = 0, theta’(0) = 0, from t = 0 to t = 60
Do the same for linear approximation
Compare the nonlinear and linear models for the following values of the frequency w: 0.6, 0.8, 1, 1.2. which frequency moves the pendulum farthest away from its equilibrium position? For which frequencies do the linear and nonlinear equations have widely different behaviors? Which forcing frequency seems to induce resonance-type behavior in the pendulum? Graph that solution on a longer interval and decide whether the amplitude goes to infinity.
13. In this problem, we consider the long term behavior of solutions of the initial value problem
d^2*y/dt^2 + 0.2dy/dt - y + y^3 = 0.3cos(wt), y(0) = 0, y’(0) = 0
for various frequencies w in the forcing term.
Plot a numerical solution of it from t = 0 to t = 100 for each of the eight frequencies w = 0.8, 0.9 …. 1.4, 1.5
Describe and compare the different long-term behaviors you see. Due to the forcing term, all solutions will oscillate, but pay particular attention to the magnitude of the oscillations and to whether or not there is a periodic pattern to them, are there any similarities between your results for this nonlinear system and the phenomenon of resonance for linear systems with periodic forcing?
matlab以前跟着老师一步一步做过
但是现在完全不会T T
各位大神帮我看一下吧
5. in this problem, we’ll investigate the effect of damping on the pendulum, using the model:
Theta” + b*theta’ + sin(theta) = 0
Prepare simulink models that will take the value of b from a “Constant” block and
Plot the numerical solution of this differential equation with initial conditions theta(0) = 0, theta’(0) = 4, from t = 0 to t = 20.
Do the same for linear approximation:
Theta” + b*theta’ + theta = 0
Compare the linear and nonlinear behavior for the values b = 1, 1.5, and 2. Interpret what is happening physically in each case; i.e., describe explicitly what the graph says the pendulum is doing.
6. in this problem we’ll look at the effect of a periodic external force on the pendulum, using the model
Theta” + 0.05*theta’ + sin(theta) = 0.3 cos wt (*)
We have chosen a value for the damping coefficient that is more typical of air resistance than the values in the previous problem. Prepare simulink models for (*) and its linear appoximation:
Theta” + 0.05*theta’ + theta = 0.3 cos wt
The right hand side can be produced by a sine wave block (which is in the sourses library). When you install this block and left click on it to bringup the block parameters menu, you will see an amplitude box in which to insert the parameter 0.3 and a frequency box in which to insert the parameter w. note that since we have a cosine, not a sine, you also have to adjust the Phase (to pi/2, since cos wt = sin (wt + pi/2)).
Plot the numerical solution of this differential equation with initial conditions theta(0) = 0, theta’(0) = 0, from t = 0 to t = 60
Do the same for linear approximation
Compare the nonlinear and linear models for the following values of the frequency w: 0.6, 0.8, 1, 1.2. which frequency moves the pendulum farthest away from its equilibrium position? For which frequencies do the linear and nonlinear equations have widely different behaviors? Which forcing frequency seems to induce resonance-type behavior in the pendulum? Graph that solution on a longer interval and decide whether the amplitude goes to infinity.
13. In this problem, we consider the long term behavior of solutions of the initial value problem
d^2*y/dt^2 + 0.2dy/dt - y + y^3 = 0.3cos(wt), y(0) = 0, y’(0) = 0
for various frequencies w in the forcing term.
Plot a numerical solution of it from t = 0 to t = 100 for each of the eight frequencies w = 0.8, 0.9 …. 1.4, 1.5
Describe and compare the different long-term behaviors you see. Due to the forcing term, all solutions will oscillate, but pay particular attention to the magnitude of the oscillations and to whether or not there is a periodic pattern to them, are there any similarities between your results for this nonlinear system and the phenomenon of resonance for linear systems with periodic forcing?