In all three cases, the force $F$ is applied directly to the free end of an ideal (massless) spring.
Fundamental Property: For a massless spring, the tension is uniform throughout its length and is equal to the external force applied at its end, regardless of the state of motion of the system (static, accelerating, or moving with friction).

According to Hooke’s Law, the extension $x$ is directly proportional to the tension $T$ in the spring: $$T = k x$$ Since the tension $T$ is equal to the applied force $F$ in all three cases: $$F = k x_1$$ $$F = k x_2$$ $$F = k x_3$$

Comparing the equations: $$x_1 = \frac{F}{k}, \quad x_2 = \frac{F}{k}, \quad x_3 = \frac{F}{k}$$ Therefore: $$x_1 = x_2 = x_3$$