Question

 A mass m at the end of a spring oscillates with a frequency of 0.83 Hz. When an additional 780-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?

 

 

Answer 1

$T_1=\frac{1}{\nu_1}=2\pi\sqrt{\frac{m}{k}}\to\frac{1}{0.83}=2\pi\sqrt{\frac{m}{k}}$

$T_2=\frac{1}{\nu_2}=2\pi\sqrt{\frac{m+0.78}{k}}\to\frac{1}{0.6}=2\pi\sqrt{\frac{m+0.78}{k}}$

$\frac{0.6}{0.83}=\sqrt{\frac{m}{m+0.78}}\to0.52257=\frac{m}{m+0.78}\to m=0.854\ (kg)=854\ g$ . Answer