What is the period of the spring's motion after the car strikes it?

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SUMMARY

The period of the spring's motion after an 870 kg car strikes it at a speed of 16 m/s and compresses it by 10.0 m can be calculated using the formula T = 2π√(m/k). In this case, the mass (m) is 870 kg, and the spring constant (k) is determined to be 2227.2 N/m. The calculated period is approximately 3.92 seconds, but since the spring only needs to stop the car, the effective time is halved to 1.96 seconds. A correction factor of 0.25 was applied to achieve the correct result.

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A 870·kg car strikes a huge spring at a speed of 16·m/s, compressing it 10.0·m.

How long does it take the spring to stop the car?
2. Homework Equations - T= 2pi√m/k
I don't know why I can't get this problem right. I have 2pi√870/2227.2=3.92 then you would divide that by 2 because it's half the period to get it stopped which gives me 1.96 which doesn't work.
 
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Just solved it, not sure why I had to multiply it by .25 instead of .5 but I took a guess and it worked.
 

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