Under the action of random exciting displacement

the response of a simple pendulum with large displacement was studied in this paper by means of nonlinear spectral analysis. It is not necessary to have the nonlinear term linearized in this method

so that the errors introduced by linearization can be eliminated. The study indicates that the linearized solution gives reasonable approximation when the displacement being small. When the displacement becomes large enough

the errors introduced by linearization increase significantly. Therefore

the nonlinear effect due to large displacement should be taken into consideration.