An asymptotic perturbation solution for a linear oscillator of free damped vibrations in
fractal medium described by local fractional derivatives was obtained in Yang and Srivastava (Commun Nonlinear Sci Numer Simul 29(1–3):499–504, 2015). In this paper, we
obtain the numerical solution of damped forced oscillator problems by employing the
operational matrix of integration of Bernoulli orthonormal polynomials. The operational
matrix of integration is determined with the help of the integral operator on Bernoulli
orthonormal polynomials. Numerical examples of two diferent problems of spring are
given to delineate the performance and perfection of this approach and compared the
results with the exact solution.