Consider two vibrating strings connected at x = L to a spring-mass system on a vertical...

Consider two vibrating strings connected at x = L to a spring-mass system on a vertical frictionless track as in Fig. 4.3.4. Assume that the spring is un stretched when the string is horizontal (the spring has a fixed support). Also suppose that there is an external force f(t) acting on the mass m.

(a) What “jump” conditions apply at x = L relating the string on the left to the string on the right?

(b) In what situations is this mathematically analogous to perfect thermal contact?