Initial Values

  • #1
Hi, World!! Nice place here! My first post in this forum. :smile:

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]?
 
Last edited:

Answers and Replies

  • #2
Hey, Guys...why silence?
Did I ask nonsense? :uhh:
I don't think it's nonsense. :grumpy:
In the meantime I came across some info on oscillations in Feynman's lectures.
It says we cannot specify acceleration with which the motion started because it is determined by the spring, once we specify [itex]x_0[/itex]. But isn't the velocity also dependent on the properties of the spring then?
 

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