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PHY.K02UF Molecular and Solid State Physics | ||||
An object moving in one-dimension can be described in terms of its position x and and its velocity v_x. If the force on the object is known, then the motion can be described by two first order differential equations,
\large \frac{dx}{dt}=v_x and \large \frac{dv_x}{dt}=a_x=F_x(x,v_x,t)/m.
Here F is the force, m is the mass, and t is the time. The form below can be used to numerically integrate these equations for a total number of N_{steps} steps using a step size of \Delta t. The acceleration a_x can be given as a function of x, v_x, and t.
$v_x$ | -1.0 -0.5 0.0 0.5 1.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 | |
$x$ |