Hi All,
Just wanted to check to see if I am doing this correctly
If the equation is
\(F(t) = m\ddot{y}+c\dot{y}+ky\)
\(\dot{y}(0) = 0\)
Where m = 1.5 c =190, k=28, F(t) = -500sin(10t)
I know that it has to be in the form of
\(yk+1 = yk+f(xk,yk)h\)
So solving Eulers method to 0.2 with a step size of 0.1
\( -500sin(10x)= 2\ddot{y}+180\dot{y}+25y\)
Now to change into for f(x,y) I have done the following
\(f(x,y) = -500sin(10x)-2\ddot{y}-180\dot{y}-25y\)
Is this the correct equation for f(x,y)??
So for i = 0
\(yk+1 = yk+f(xk,yk)h\)
\(y1 = yo+f(xo,yo)h\)
where
x0 = 0
y0 = 0
h = 0.1
This is where I think I have made a mistake becuase the two answers that I have found are very different from one another. I would like to know if I have done this correclty.
\(y1 = 0 + f(0, 0)0.1\)
\(y1 = 0 + f(-500sin(10*0)-2*0-180*0-25 )*0.1\)
\(y1 = -2.8\)
and for i = 1
\(y2 = y1+f(x1,y1)h\)
\(y1 = 1 + f(1, 1)0.2\)
\(y1 = 1 + f(-500sin(10*1)-2*1-180*1-25 )*0.2\)
\(y1 = -60.26tex]
Have I used eulers method correctly to solve for y1 = -2.5, y2 = -58.76
Thanks for your time\)
Just wanted to check to see if I am doing this correctly
If the equation is
\(F(t) = m\ddot{y}+c\dot{y}+ky\)
\(\dot{y}(0) = 0\)
Where m = 1.5 c =190, k=28, F(t) = -500sin(10t)
I know that it has to be in the form of
\(yk+1 = yk+f(xk,yk)h\)
So solving Eulers method to 0.2 with a step size of 0.1
\( -500sin(10x)= 2\ddot{y}+180\dot{y}+25y\)
Now to change into for f(x,y) I have done the following
\(f(x,y) = -500sin(10x)-2\ddot{y}-180\dot{y}-25y\)
Is this the correct equation for f(x,y)??
So for i = 0
\(yk+1 = yk+f(xk,yk)h\)
\(y1 = yo+f(xo,yo)h\)
where
x0 = 0
y0 = 0
h = 0.1
This is where I think I have made a mistake becuase the two answers that I have found are very different from one another. I would like to know if I have done this correclty.
\(y1 = 0 + f(0, 0)0.1\)
\(y1 = 0 + f(-500sin(10*0)-2*0-180*0-25 )*0.1\)
\(y1 = -2.8\)
and for i = 1
\(y2 = y1+f(x1,y1)h\)
\(y1 = 1 + f(1, 1)0.2\)
\(y1 = 1 + f(-500sin(10*1)-2*1-180*1-25 )*0.2\)
\(y1 = -60.26tex]
Have I used eulers method correctly to solve for y1 = -2.5, y2 = -58.76
Thanks for your time\)
Last edited: