Question

The period of a mass-on-spring oscillator is 3 seconds. Upon decreasing its mass by 500 g, the period will become 2 seconds.

a) Calculate the original mass!

b) Calculate the spring constant! 

Could you please explain in detail how to use the equation below?

$$T=2\pi√m/k$$

Answer 1

a)

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

$T_1=2\pi \sqrt{\frac{m-m_1}{k}},\implies$

$m=\frac{m_1T^2}{T^2-T_1^2}=\frac{0.5\cdot 9}{9-4}=0.9~kg,$

b)

$k=\frac{4\cdot 3.14^2\cdot 0.9}{9}=3.95~\frac{N}{kg}.$