Ok, I have discovered the error. The restoring force F2 should also be upwards. Spring 2 also wants to bring the mass to its equilibrium position even if it is a pull spring.
The question around the negative energy of the spring is also solved.
Thanks.
Lets say the resting equilibrium position for the springs are x1 and x2. The reason why they have to be prestressed is because they are pull springs. They can only have a force in one direction. They both are pulling at any time at the mass. When they are not prestressed then, at the position...
Consider a mass m with a prestressed pull spring on either end, each attached to a wall. Let k1 and k2 be the pull spring constants of the springs. A displacement of the mass by a distance x results in the first spring k1 lengthening by a distance x(and pulling in the - direction), while the...