Answer to Question #98787 in Mechanics | Relativity for Sylvernus Osagu

Question

1) A spring connected to a mass of 0.15 kg has a period of oscillation of 0.408 seconds. What is spring constant?
2) A spring with a force constant of 45.5 N/m oscillates with a period of 0.908 seconds. What mass must be attached to the spring?
3) A spring with a force constant of 44.5 N/m is connected to a mass m. If the period of oscillation is 1.094 s, what is the mass?

Answer 1

1) Spring stiffness $k = m(\frac{2\pi}{T})^2 = 35.5 (N/m);$

2) Desired mass $m = k(\frac{2\pi}{T})^{-2} = 0.92 (kg);$

3) Desired mass $M = k(\frac{2\pi}{T})^{-2} = 1.35 (kg).$