What mass should be attached to a vertical spring (k = 39.5 N/m) so that the natural vibration frequency of the system will be 1.00 Hz?
A) 39.5 kg
B) 2.00 kg
C) 1.00 kg
D) 1.56 kg
E) 6.29 kg

Question

Quizplus · Accepted Answer

The natural vibration frequency $f$ of a mass-spring system is given by $f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$, where $k$ is the spring constant and $m$ is the mass attached to the spring. Rearranging this formula to solve for $m$ gives $m = \frac{k}{(2\pi f)^2}$. Substituting $k = 39.5 \, \text{N/m}$ and $f = 1.00 \, \text{Hz}$ into this formula yields $m = 1.00 \, \text{kg}$.

What Mass Should Be Attached to a Vertical Spring (K