SOLUTION: The period T of the motion of a body of mass M at the end of a spring with spring constant k is given by: T=2𝜋√M/k Use the experimentally determined values 𝑀= (210

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Question 1181819: The period T of the motion of a body of mass M at the end of a spring with
spring constant k is given by:
T=2𝜋√M/k
Use the experimentally determined values
𝑀= (210± 5)𝑔
𝑇 =(1.1±0.1)𝑠
to calculate k and the error in k.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
T+=+2%2Api%2Asqrt%28M%2Fk%29
===> 1.1+=+2%2Api%2Asqrt%28210%2Fk%29 upon direct substitution.
==> sqrt%28k%29+=+%282%2Api%2Asqrt%28210%29%29%2F1.1+
===> highlight%28k+=+6851.63%29, using appropriate units.
Then using the differential for T,
===> dT+=+T%5BM%5D%2AdM+%2B+T%5Bk%5D%2Adk
= %28pi++%2Fsqrt%28M%2Ak%29%29%2AdM+-+%28%28pi%2Asqrt%28M%29%29%2Fk%5E%283%2F2%29%29%2Adk
===>
===> 0%2B-+0.1+=+0%2B-+0.0131+-+0.00008%2Adk

===> 0%2B-+0.0869+=+-0.0000803%2Adk
===> dk = -+ 1082.2, to 2 d.p.