proportional to their displacement from equilibrium. Such a system will
oscillate in simple harmonic motion if released (in theory and to a level
of approximation in practice). The ODE representing this is:
m x'' = -k x
where m is the effective mass of the body attached to a light spring, and
k is the spring constant.
However we also observe that the oscillations decay in practice, and that
a reasonable representation of this is obtained by introducing a speed dependent force opposing the motion. Now the ODE becomes:
m x'' = -kx - cx'
where now c is a constant characterising the damping.
Now if an external force F(t) is applied to the system the ODE becomes:
m x'' = -kx -cx' + F(t)
which is what you have.