Cyclic frequency of unknown weight

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SUMMARY

The discussion centers on calculating the cyclic frequency of a spring-mass system where an unknown weight W is suspended from a spring with an unknown force constant k. The spring stretches 14.2 cm due to weight W, and after being pulled down an additional 1.8 cm, it oscillates. The correct calculation for the spring constant k is derived from the equilibrium position, leading to k = 9.8 m / 0.142 m = 68.87 N/m. The period T is calculated using T = 2π√(m/k), resulting in a frequency of approximately 3.714 Hz, which is confirmed to be incorrect due to the miscalculation of k.

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  • Basic algebra for manipulating equations
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When an unknown weight W was suspended from a spring with an unknown force constant k, it reached its equilibrium position and the spring was stretched 14.2cm because of the weight W. Then the weight W was pulled further down to a position 16cm (1.8cm below its equilibrium position) and released, which caused an oscillation in the spring. Calculate the cyclic frequency of the resulting motion. Answer in Hz.

I set k=F/x:
k=9.8m/.018 = 544.44m

I used T=2π√(m/k) to solve for the period:
T=2π√(m/544.44m) = .269s The mass canceled out

I did 1/T for frequency:
1/.269 = 3.714Hz

The answer is wrong. I think it might have something to do with the 14.2cm information but I don't know how to incorporate it in the problem.
 
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You need to use the 14.2 cm to calculate the spring constant.
 

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