So we know that too calculated force when the spring is compressed, will be the spring. Constant times. Thie compression. So let's say initially, the spring is in this state. And then after confession, the spring is compressed, and that's the extra amount ofthe distance that the spring traveled. So if we say that initially the spring is in position X one and after compression it's in the position of ex too. Then we can say that F easy hold. Okay, Times X to minus X one. Now we're given the work done due to the compression, which is Etienne. Jules. Now, since we know the work done due to the compression will try toe relate. This worked on with the spring constant and the compression so that we get the force out of it. So what I mean by that is we know that if the spring is an initial position next one and it's been compressed to a position x two, then the amount ofthe work done is it Has Kate X two squared minus half off key X one squared right. And from there, a cz we say that we already know the work done. So we can actually try to solve for key from this expression and using that key valley, we can actually figure out the force. Now, one thing that we should notice here is initially when the spring is un compressed, we can consider X 10 So if X one is zero, then we can get you off. This time on, we can get you this time over here Now from that, if we try to solve for key, we see that cans equal to times W divided by X two xk red Right on DH. Here the question will be f equals K times x two. Now we can see that if this is the positive extraction, then since it's compressed, we can take extras negative. And we know that the compression is 0.2 meters. So in anarchist X two will be zero point negative zero point two meter. We can use this value to figure out K and using that I came alone, we can solve for the force. So let's do that. Let's write that the expression in terms of work than one more time. So we have X two squared Now if we use the values given So we have the jewels for the world turns and for the displacement. It's negative 0.2. But we can get you out of that negative sign because there's a square here. So even if it's negative, it will be a positive overall. So we can write 0.2 meters and then miss where it's so. Finally, the spring constant will be for 1,000 Newton or meter using that cable we can solve for the force, which is Kate Times X two. So the force will be 4,000 Newton for meteor times X to which is negative 0.2 meter. Using that, we see that the forces negative 800 Newtons and we can say that the magnitude off the force it is 800 mutants now. In the second case, the spring is further compressed down toe 0.4 meters because initially the spring was here from the there that it's been complaints too. 0.2. Then it's been further compressed down. Toa let me draw it here around this position, so the distance from here tto The final position will be 0.4 meters right because it's further compressed down 2.0 toe point toe. So we add point, too, with the previously compressed point. Oh, that's why we got 00.4 meters there. But again that the negative so we can do the similar argument here. Now we'll have x one, a zero on extra as negative 0.4 meters. Amazing that relation. We can again figure out the work done, which is have key X two squared minus half off kids one squared and again we can get it up this time because X one is zero. So from there we see that the Wharton is half off. He is 4,000 Newton per meter, so that's 4,000 per meter. And x two is again a sense. It's a square, so we don't have to worry about the negative sign here. We can just take the magnitude of ex, too, and that's 0.4 squared and combining this, we get the work done as 3 20 Jews. All right, so that's the amount of work done to the spring after it's been compressed to a 0.4 meters. But then the additional work Ah, let's call it W ad. So add means Theoden Ishan ofwork. So the addition and work will be the previous the total work, which is 3 20 Jules minus the worked and do tow the spring being compressed toe 200.2 meters. So this is the additional amount of work, which is 2 40 Jules, right? Um, and for the force, it's going to be again f f equals K Times X, where Katie's 4,000 noon per meter and exes negative 0.4 meter. Using that, we see that the forces negative 1,600 mutants. And if you just if we just take the magnitude ofthe earth, that's going to be 1,600 Nunes. So notice one thing. There we. When we compressed the spring to Onley 0.2 meters, we saw that the work done was on ly 80 jewels. But then when it was when the compression was doubled, Or in other words, when the compression was 800.4 meters, we saw that the worked and was 3 20 Jules and ah, that is that That means that we it's not the world and it's not double, but instead it's actually increasing, um, four times because we see that there's a relation of X squared over here. So if the distance is doubled the work and is four times the previous work. So that's why we had four times the work. And when the spring was compressed toe twice the emission compression. Thank you.