To find the spring constant $$(k)$$ of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in measurement of mass. The percentage error in determining value of $$k$$ is :

Find percentage error in spring constant $$k$$ given 2% error in time and 1% error in mass.

Relation between k, m, and T.

$$T = 2\pi\sqrt{\frac{m}{k}}$$, so $$k = \frac{4\pi^2 m}{T^2}$$.

Error propagation.

$$\frac{\Delta k}{k} = \frac{\Delta m}{m} + 2\frac{\Delta T}{T} = 1\% + 2(2\%) = 1\% + 4\% = 5\%$$

Note: we take absolute values of errors for maximum percentage error regardless of sign.

The correct answer is Option A: 5%.