- #1
littleHilbert
- 55
- 0
Hi, World! Nice place here! My first post in this forum. 
I've got a short question for a start.
If we wish to evaluate the constants for the general solution
x(t)=C_1e^{-{\lambda_1}t}+C_2e^{-{\lambda_2}t}
of this ODE:
\ddot{x}+2{\gamma}\dot{x}+{{{\omega}_0}^2}x=0
we can choose the initial conditions: x(0)=x_0,\dot{x}(0)=v_0
I cannot see at a glance why we can't choose an initial condition of acceleration and try to calculate the constants using this value. Why do we choose x_0,v_0 and not for example x_0,a_0 with a_0={{\lambda_1}^2}C_1+{{\lambda_2}^2}C_2?
I've got a short question for a start.
If we wish to evaluate the constants for the general solution
x(t)=C_1e^{-{\lambda_1}t}+C_2e^{-{\lambda_2}t}
of this ODE:
\ddot{x}+2{\gamma}\dot{x}+{{{\omega}_0}^2}x=0
we can choose the initial conditions: x(0)=x_0,\dot{x}(0)=v_0
I cannot see at a glance why we can't choose an initial condition of acceleration and try to calculate the constants using this value. Why do we choose x_0,v_0 and not for example x_0,a_0 with a_0={{\lambda_1}^2}C_1+{{\lambda_2}^2}C_2?
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