Yes this can be done, but there are multiple ways of doing this.
For once you can use the Block "Spring and Damper Force". There you can set the inital length, Spring siffness and Damping Coefficient. Just connect two not ridgidly connected frames. With this setting the initial position to be not in the relaxed state seems to be a bit tricky.
The in my opinion smarter way is to use a "Prismatic Joint" Block only. In the block settings you can directly define Equilibrium Position, Spring Stiffness and Damping Coefficient. By Setting Equilibrium Position to a Value other than 0 you set up the spring-damper-system in a non relaxed state (which is in your case desired).
The attachment is simulink-file with two prismatic joints set up in a way like your example.
