68

S.B. Karavashkin, O.N. Karavashkina

Suppose that zero of the distributed line is the location of  n + 1-st mass of a lumped line in unexcited state. Then

where x_k is the external force application point, and  are the wave propagation velocities in the sections having related densities ₀₁  and ₀₂ .

Substituting (41) to the base system and finding the limit at a 0 , we yield the sought solution:

for the section x₀ x_k

We see from (42) - (44) that at the limit passing, the line with distributed parameters remains its distinctions considered above for a lumped line.