$13\mathrm{.}36$ A jet engine with a mass of $272$ kg is tested on a stand, which results in a natural fre$-$

quency of $26$ Hz $.$ The spectral density of the jet force under test is shown in Fig. P$13\mathrm{.}36.$

Determine the probability of the vibration amplitude in the axial direction of the jet

thrust exceeding $0\mathrm{.}012$ m $.$ Assume zeta$=0\mathrm{.}10.$

FIGURE P$13\mathrm{.}36.$

give me mathematical solution for mechanical vibration subject