Damped mass-spring system

A mass $m$ is attached to a linear spring with a spring constant $k$. The spring is stretched 2 cm from its equilibrium position and the mass is released from rest. A drag force acts on the mass that is in the opposite direction as the velocity $F_{\text{drag}}=-bv_x$ where $b$ is the drag force constant. The acceleration of the mass is $a_x=-kx/m-bv_x/m$. The motion is in a line which we can take to be the $x$-axis. The oscillations of a damped mass-spring system can be determined using a numerical differential equation solver. Adjust the mass, the spring constant, and the damping constant to get underdamped and overdamped oscillations.

$m=$ 1 [kg]

$b=$ 0.2 [kg/s]

$k=$ 0.9 [N/m]

The period of the oscillations is $T=2\pi/\sqrt{\frac{k}{m}-\frac{b^2}{4m}}=$ 6.66 s.

   

 Numerical 2nd order differential equation solver 

$ \large \frac{dx}{dt}=$

$v_x$

$ \large a_x=\frac{F_x}{m}=\frac{dv_x}{dt}=$

Intitial conditions: 

$x(t_0)=$

 

$\Delta t=$

$v_x(t_0)=$

 

$N_{steps}$

$t_0=$

 

Plot:

vs.

 

 $t$       $x$      $v_x$