A ball is thrown vertically upward

A ball is thrown vertically upward with an initial velocity of $v_0=10$ m/s. There is a velocity dependent drag force directed in the opposite direction to the velocity. The total force on the ball is gravity plus the drag force $F=-mg-bv_x$, where $F$ is the force, $m$ is the mass of the ball, $g=9.81$ m/s² is the acceleration of gravity at the earth's surface, $b$ is the drag force constant, and $v_x$ is the velocity. The motion is in a line which we can take to be the $x$-axis. The differential equation that describes this motion is $m\frac{d^2x}{dt^2}+b\frac{dx}{dt}=-mg$. The equations are loaded into the analytic second order differential equation solver below.

$m=$ 1 [kg]

$b=$ 0.4 [kg/s]

For long times, the ball falls with a constant terminal velocity $v_{\text{terminal}}=-mg/b=$ -24.5 m/s.

 Linear 2nd order differential equation solver 

\( \large m\frac{d^2x}{dt^2}+ b\frac{dx}{dt}+kx = F_0, \)

$m=$

$b=$

$k=$

$F_0=$

 

Initial conditions:

$x(t_0)=$

$\frac{dx}{dt}(t_0)=$

$t_0=$