Recent content by Meteorologist

Yes, any changes to the characteristic equation could yeild large differences in the solution. The exponential term i had out in front that you are referring too was simply a factored out term. And yes again, if the coefficient of the first derivative term equals zero then alpha would then be...

Cyosis, Absense of a first derivative really has nothing to do with whether or not exponentials will be in the answer. as far as i know an equation such as that will always have a constant times an exponential in the solution. In this case there is no exponential because it is raised to the...

Cyosis, i believe the reason for multiplying e^(alpha*t) by (Acos(beta*t) + Bsin(beta*t)) is becasue when solving an ODE with imaginary roots you are left dealing with an exponential of the form e^(alpha + i*beta). This can be expanded into a form involving sines and cosines. If you would...

Is this all the given information?

pbandjay, I guess there is no exponentials in your final answer becasue the solution should be in the form: y(t)=e^(alpha*t)*(Acos(beta*t) + Bsin(beta*t)) Where i guess in this case: alpha=0 (Therefore making e^(alpha*t) equal to 1) beta=sqrt(k) Just trying to understand your logic...