I've completed my Engineering but doing a self study course in Dynamics of Structures and have got a very fundamnetal question concerning solution of differential equation and hope someone will be able to help me.(adsbygoogle = window.adsbygoogle || []).push({});

Sorry if its too fundamnetal and stupid!

Let us say we have to solve a differential equation:

mu_double_dot + k_u=0

(double dot indicates second derivative)

We put,

u = e^st

we get first and second order derivative of u and substitute in the abovce differential equation and get:

s = +i sqrt(k/m) or -i sqrt(k/m)

We now say that general solution is:

u = A1 e^s1t + A2 e^s2t

where s1 and s2 are +i sqrt(k/m) and -i sqrt(k/m) respectively

Shouldn't the solution be:

u = e^s1 tORu = e^s2t ??

Please can anyone help what is the logic in putting

u = A1 e^s1t + A2 e^s2t and why?

Vishal

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# Fundamental- solving a second order differential equation

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