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: