High in the given problem. The mass, which is oscillating with the help off the spring on the horizontal platform, is given ence must off the block. MM is equal to 0.400 kg and force constant off. The spring is K is equal to 200 Newtons for meter. No, when the displacement instantaneous displacement off the block from it's mean position is let it be vile, and that is given as 0.1 60 m. Then the speed off the block at that moment is we is equal to 3.0 meter per second. Now, in the first part of the problem, we have to find the maximum speed off the block. Then it will be passing through its mean position. So to find this maximum speed off the block, first of all, using the expression for its instantaneous velocity, which says we is equal toe Amira, the angular, frequency off oscillation square root off a square. Maximum displacement off the block means amplitude off facility emotion minus y squared. And here key is given us am Omega Square. So using that omega squared equals Tokyo. I am, or we can say omega is equal to square root off Gabe, I am so putting this value formula Also here in the expression for instantaneous velocity we get, we is equal to square root off cape I am into square root off a square, minus wise. Where or we can say this is square root off e g Break it a square minus y squared by m No squaring Botha sires we get so we square is equal. Tok is square minus y squared, divided by m muscle the block so plugging in the non values hair for V, the speed off the block that was given us 3 m per second. So that's the square will come out to be nine is equal to four k. This is 200 a means maximum displacement off the block means an amplitude off the oscillator emotion that is not given to us. So it remains as is well minus. Survive means the instantaneous displacement which is 0.16 to the whole square, divided by mass off the block, which is 0.400 kg. So this 200 into a square minus for this 0.1 60 square it comes out to be 0.256 visible to nine in 20.4, which comes out to be 3.6. Or this a square minus 0.256 becomes equal to 3.65 200 which comes out to be 0.18 Hence, a square becomes 010 to 56 plus 0.18 means it comes out to be 0.436 So amplitude off this facility emotion with the square root off 0.0 436 m. Or we can say this is 0.209 m. Hence, the maximum miss speech off the block after its mean position will be given by the product office amplitude with it's angular frequency a Oh, make up what you can say. This is 0.209 for Omega. This is square root off. Gabe. I m k is 200. Bye. Mm. We choose 0.4, so it comes out to be 0.209 Removing this decimal 2000 by four which becomes square root off 500 So finally, this ReMax needs the answer off. First part of the problem comes out to be 4.67 m. But second answer for the first part of the problem, no. In the second part of the problem, we need to find the magazine experience, after which the spring is compressed and that is actually ableto complete your off the social promotion. So maximum dispense. Bye, bitch. The spring is compressed is its amplitude which we have found already and that is 0.209 meter and the third part of the problem actor Maximum compression. We have to find speed off the block and acceleration of the block. So at maximum compression, speed off the block will be zero and its acceleration means capitally will be given by in magnitude. It'll be given by a into Omega Square. So it becomes 0.209 into square off omega, which was square root off 200 by 0.4. So simply it will become hunted by 0.4 square would be removed due to this squaring. So it comes out to be into 500. So this is 0.209 into 500 meter per second square. Or you can say this is 104.5 meter per second squared. Answer for the third part off the problem. Thank you.