I\'m doing a lab report and we are seeing two different methods of calculation t

Question

I'm doing a lab report and we are seeing two different methods of calculation the spring constant The first method being to measure the extension of the spring in response to force (force/mass vs displaced distance) and the second method being to observe the oscillation period to displacement (T to the square root of the mass acting on the spring). We will be seeing which method yields a more accurate springs constant.

For method one we got a spring constant: 5.9

Method 2 k=9.026

In general can you explain which method is more accurate and why? I feel like the second one is because we used more video analysis and less room for human error but I'm wondering if there are some more mathematical answers I can use to justify this. Also, how would I calculate a theoretical k value to compare them too?

Explanation / Answer

method one seems to be more accurate. The reason being, while oscillating, the air also provides resistance which generally is not considered in the calcultaions. Resistance due to air alters the period of oscillation and therefore determining k based on oscillation without considering air resistance might be more prone to error.

This is not the case in forst method since the method is based on static equilibrium . Hence, when a load is applied, the spring's length alters. Based on this the spring constant k can be easilty calculated.the only room for error in this method is human error in taking measurements to determine the change in length of spring

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