Answer to Question #276150 in Physics for Kai

Question

1. Determine the period of oscillation of an ideal spring with mass 22.1kg and spring constant 27.8N/m. 
2. A mass of 9.2kg is attached to an ideal spring having a force constant of 270.3N/m as in the figure. The mass is displaced from its equilibrium position and released. Assume negligible friction. What is the mass' frequency of oscillation?
3.  A mass of 6.1kg is attached to a spring having a force constant of 219.1N/m as in the figure. The mass is displaced from its equilibrium position and released. Assume a damping force constant b=16.3kg/s, what is the mass' frequency of oscillation? 

Answer 1

1)

$$T=2\pi\sqrt{\frac{22.1}{27.8}}=5.60\ s$$

2)

$$\frac{1}{f}=2\pi\sqrt{\frac{9.2}{270.3}}\\f=0.86\ Hz$$

3)

$$f=\frac{1}{2\pi}\sqrt{\frac{219.1}{6.1}-\frac{16.3^2}{4(6.1)^2}}\\f=0.93\ Hz$$