Differentials

• Feb 20th 2010, 12:43 AM
IBD
Differentials

http://img2.immage.de/200270494rszexercise2.jpg
• Feb 20th 2010, 01:02 AM
Prove It
Quote:

Originally Posted by IBD

http://img2.immage.de/200270494rszexercise2.jpg

What's the exercise?
• Feb 20th 2010, 01:11 AM
IBD
Thanks for looking into my problem Prove It. I have inserted a picture of the exercise but it seems that you could not see it. I have now uploaded it as an attachment. Thanks again
• Feb 20th 2010, 01:39 AM
Prove It
Why not substitute D and S into the equation for \$\displaystyle p''\$?

This will give you a second order constand coefficient ODE.
• Feb 20th 2010, 09:16 PM
IBD
Thanks Prove it for your response. I will substitute into p'' however i don't get p' this way. could you please let me know how i will obtain the differential equation that the first question asks for?
• Feb 20th 2010, 09:31 PM
Prove It
Quote:

Originally Posted by IBD
Thanks Prove it for your response. I will substitute into p'' however i don't get p' this way. could you please let me know how i will obtain the differential equation that the first question asks for?

You should end up with

\$\displaystyle p''(t) = a[d_0 + d_1p(t) - (s_0 + s_1p(t))]\$

Solve the homogeneous characteristic equation:

\$\displaystyle m^2 + as_1 - ad_1 = 0\$

\$\displaystyle m^2 = ad_1 - as_1\$

\$\displaystyle m^2 = a(d_1 - s_1)\$.

Now since \$\displaystyle d_1 < 0\$ and \$\displaystyle s_1 > 0\$, this means \$\displaystyle d_1 - s_1 < 0\$.

Also, since \$\displaystyle a > 0\$, this means \$\displaystyle a(d_1 - s_1) < 0\$.

So you have \$\displaystyle m^2\$ equaling a negative number. What does this tell you about \$\displaystyle m\$? Can you solve the DE now?
• Feb 20th 2010, 11:30 PM
IBD
My dearest Prove It can you please send me a pm with some contact information (email)? I cannot send you a pm because I am a new member and don't have 15 posts. I need to discuss something in private. Thanks