- #1
svishal03
- 129
- 1
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.
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 t OR u = e^s2t ??
Please can anyone help what is the logic in putting
u = A1 e^s1t + A2 e^s2t and why?
Vishal
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 t OR u = e^s2t ??
Please can anyone help what is the logic in putting
u = A1 e^s1t + A2 e^s2t and why?
Vishal