Green’s function approach to inhomogeneous Lamb problem: response to a sudden impulse

The response of the oscillator in a Lamb problem made of two semi-infinite strings of different mass densities to a sudden impulse is obtained using the Green’s function method. It is shown that after delivering the impulse, the oscillator emits decaying waves along both sides of the string leading to the radiation damping for the oscillator. It is pointed out that for the oscillator coupled at the joining point of the strings, the damping factor of the wave is proportional to the sum of the impedances of the strings. When the difference between the densities vanishes, the result is in agreement with the result known for the homogeneous model.