Why did they do 1/4 T in the last part. Please and thank you A 0.98 kg block sli

Question

Why did they do 1/4 T in the last part. Please and thank you

A 0.98 kg block slides on a frictionless horizontal surface with speed 1.32m/s. The block encounters an unstretched spring with force constant 245N/m, as shown. a) how far is the spring compressed before the block comes to rest? b) how long is the block in contact with the spring before it comes to rest? c) how far is the spring compressed when the kinetic energy of the block is equal to the potential energy stored in the spring? For part b) we can use the formula for the period of oscillation of a mass-on-a-spring: T = 2 pi Squareroot m/k In this case we only want 1/4 of the period. T = 2 pi Squareroot 0.98kg/245 N/m = 0.4 sec 1/4 T = 0.1 sec

Explanation / Answer

T represent the time period of the oscillation which is the time elapsed in one cycle (that is, going from mean position to extreme end (where it stops) then coming back to the mean position and then going to the other extreme end and then finally coming back to the initial mean postion) of oscillation to complete.

Now , in the part you have asked about , the block is going from initial mean position ( that is, when the block first strikes the spring ) to one extereme end of oscillation (where it stops). So, this includes only 1/4 of the total cycle of oscillation , therefore T/4 is the answer.

Hope it helps. please provide feedback. thankyou.

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