How can I calculate the potential energy stored in a compressed spring?

[dge]

Homework Statement

Two identical blocks, A and B, on a frictionless surface are connected by a spring of negligible mass. The spring is initially unstretched. During the interval from t1 to t2, block A is pushed through a distance dA by a hand exerting a force of magnitude FA, as shown. Block B is held in place by a wall. The wall exerts a force on block B that varies with time but is always directed to the left.

Write an expression for the net external work done on system ABS by external forces in terms of given quantities (ie. FA, dA, and/or t2). Explain.

Relevant Equations

Work = Force * displacement

I feel like I've gotten stuck on this. I know the work done is equal to the kinetic energy of block A, but I can't figure out how I would find the potential energy stored in the spring without using the spring constant in the equation. W = FA * dA + U

 

[haruspex]

Homework Statement:: Two identical blocks, A and B, on a frictionless surface are connected by a spring of negligible mass. The spring is initially unstretched. During the interval from t1 to t2, block A is pushed through a distance dA by a hand exerting a force of magnitude FA, as shown. Block B is held in place by a wall. The wall exerts a force on block B that varies with time but is always directed to the left.

Write an expression for the net external work done on system ABS by external forces in terms of given quantities (ie. FA, dA, and/or t2). Explain.
Relevant Equations:: Work = Force * displacement

the work done is equal to the kinetic energy of block A,

That’s the work done on block A, but it is not the work done on the system "ABS" (S presumably being the spring).
You do not need to care how the work done on the system gets partitioned into KE and EPE.

 

[dge]

That’s the work done on block A, but it is not the work done on the system "ABS" (S presumably being the spring).
You do not need to care how the work done on the system gets partitioned into KE and EPE.

So would it just be the force applied * the displacement?

 

[haruspex]

So would it just be the force applied * the displacement?

Yes.

 

[dge]

Yes.

I guess I overcomplicated that in my head. Thank you!