- #1
sristi89
- 8
- 0
Hi,
Here is the equation:
x+x'=5.1sin(600*t)*u(t)
Our teacher gave us a hint that we should try using a substitution which is a system of sines, cosines, and looks something similar to 5.1sin(600*t)*u(t).
I tried substituting:
x(t)= A sin (w1*t)+B cos (w2*t)+ c cos(w3*t)*u(t)
By differentiated this I get:
x'(t)=A*w(1)*cos(w1*t)-B*w2*sin(w2*t)-c*w3*sin(w3*t)*u(t)+c cos(w3*t)*u'(t)
Putting everything together I have:
A sin (w1*t)+B cos (w2*t)+ c cos(w3*t)*u(t)+A*w(1)*cos(w1*t)-B*w2*sin(w2*t)-c*w3*sin(w3*t)*u(t)+c cos(w3*t)*u'(t) =5.1sin(600*t)*u(t)
Then I get 5 equations:
1) A sin (w1*t)-B*w2*sin(w2*t)=0
2) B cos (w2*t)+A*w(1)*cos(w1*t)=0
3)c cos(w3*t)*u(t)=0
4)-c*w3*sin(w3*t)*u(t)=0
5)-c*w3*sin(w3*t)*u(t)=5.1sin(600*t)*u(t)
By solving 5, I get w3=600 and c=-.0085. As there are less equations than unknowns, how do I find A, B, wi, and w2.
Also, the initial condition is x(0)=0.
Thanks
Here is the equation:
x+x'=5.1sin(600*t)*u(t)
Our teacher gave us a hint that we should try using a substitution which is a system of sines, cosines, and looks something similar to 5.1sin(600*t)*u(t).
I tried substituting:
x(t)= A sin (w1*t)+B cos (w2*t)+ c cos(w3*t)*u(t)
By differentiated this I get:
x'(t)=A*w(1)*cos(w1*t)-B*w2*sin(w2*t)-c*w3*sin(w3*t)*u(t)+c cos(w3*t)*u'(t)
Putting everything together I have:
A sin (w1*t)+B cos (w2*t)+ c cos(w3*t)*u(t)+A*w(1)*cos(w1*t)-B*w2*sin(w2*t)-c*w3*sin(w3*t)*u(t)+c cos(w3*t)*u'(t) =5.1sin(600*t)*u(t)
Then I get 5 equations:
1) A sin (w1*t)-B*w2*sin(w2*t)=0
2) B cos (w2*t)+A*w(1)*cos(w1*t)=0
3)c cos(w3*t)*u(t)=0
4)-c*w3*sin(w3*t)*u(t)=0
5)-c*w3*sin(w3*t)*u(t)=5.1sin(600*t)*u(t)
By solving 5, I get w3=600 and c=-.0085. As there are less equations than unknowns, how do I find A, B, wi, and w2.
Also, the initial condition is x(0)=0.
Thanks