littleHilbert
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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
[itex]x(t)=C_1e^{-{\lambda_1}t}+C_2e^{-{\lambda_2}t}[/itex]
of this ODE:
[itex]\ddot{x}+2{\gamma}\dot{x}+{{{\omega}_0}^2}x=0[/itex]
we can choose the initial conditions: [itex]x(0)=x_0,\dot{x}(0)=v_0[/itex]
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 [itex]x_0,v_0[/itex] and not for example [itex]x_0,a_0[/itex] with [itex]a_0={{\lambda_1}^2}C_1+{{\lambda_2}^2}C_2[/itex]?
I've got a short question for a start.
If we wish to evaluate the constants for the general solution
[itex]x(t)=C_1e^{-{\lambda_1}t}+C_2e^{-{\lambda_2}t}[/itex]
of this ODE:
[itex]\ddot{x}+2{\gamma}\dot{x}+{{{\omega}_0}^2}x=0[/itex]
we can choose the initial conditions: [itex]x(0)=x_0,\dot{x}(0)=v_0[/itex]
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 [itex]x_0,v_0[/itex] and not for example [itex]x_0,a_0[/itex] with [itex]a_0={{\lambda_1}^2}C_1+{{\lambda_2}^2}C_2[/itex]?
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