The matrix material in a linear viscoelastic, unidirectional composite material is to be modeled by using a Maxwell model having parameters \(k_{\mathrm{m}}\) and \(\mu_{m}\), whereas the fiber is to be modeled by using a Kelvin-Voigt model having parameters \(k_{\mathrm{f}}\) and \(\mu_{\mathrm{f}}\).

a. Determine the complex extensional moduli of fiber and matrix materials in terms of the Maxwell and Kelvin-Voigt parameters and the frequency, \(\omega\).

b. Determine the complex longitudinal modulus of the unidirectional composite. Assume that fiber and matrix materials are isotropic. It is not necessary to use the Fourier transforms.