The dynamic characteristics of viscoelastic material components can be approximately described by a model consisting of two springs and a viscous damper as shown in the figure on the right. Assume that the component is acted upon by a random external force f(t), and the corresponding response is x(t). Assuming that f(t) is a stationary random process, the corresponding power spectral density function is Sf (w) = So = 1+ Try to find: 1) the frequency response function corresponding to the input and output; 2) the mean square value of the response x(t). Tip: Use the coordinates of the connection point between the spring k2 and the damper as the additional coordinate y(t), thereby establishing the motion equations about x(t) and y(t), then eliminate y(t), and solve the frequency response function according to the definition. When calculating the mean square value of the response, in order to facilitate the integration using the standard integral formula, the power spectral density function can be rewritten as Sf (w) = So |1 + i f(t) x(t) k2 *1