If this oscillator is driven by a step function given by

Question

Compute the right solution of the following question

Question- Consider a 1-D linear damped oscillator described by the conventional differential equation: d²x/dt² + 2B(dx/dt) + w_o²x = 0.

Part 1- If this oscillator is driven by a step function given by F(t)/m = a for t>0, show that the general solution for this oscillator is x(t) = (a/w_o²)(1 - e^-Btcos(w₁t) - (Be^-Bt/w₁)sin(w₁t)) for t>0. The oscillator was at rest in its equilibrium position before the driving force hit.

I want help to formulate the general solution for oscillator.