Question

the percentage uncertainity in mass and spring constant in time periodof spring mass respectively are 2% and 6 % .the percent uncertainity in its time period will be
(a) 3%
(b) 4%
(c) 8%
(d) none

Answer 1

$$T=2\pi \sqrt{\frac{m}{k}}$$

$$\frac{\Delta T}{T}=\frac{1}{2}\frac{\Delta m}{m}+\frac{1}{2}\frac{\Delta k}{k}$$

$$\frac{\Delta T}{T}=\frac{1}{2}0.02+\frac{1}{2}0.06=0.04=4\%$$

Answer: (b) 4%