If a system initially rests at its equilibrium position, from where it is acted upon by a unit-impulse at the instance t =0, i.e., p (t) in the equation above is a Dirac delta function δ (t), x ( 0 ) = d x d t | t = 0 = 0 , then by solving the differential equation one can get a fundamental solution (known as a unit-impulse response function)