Increasing the spring constant k of a mass-and-spring system causes what kind of change in the resonant frequency of the system? (Assume no change in the system's mass m.)
A) The frequency increases.
B) The frequency increases if the ratio k/m is less than or equal to 1 and decreases if the ratio k/m is greater than 1.
C) The frequency increases if the ratio k/m is greater than or equal to 1 and decreases if the ratio k/m is less than 1.
D) The frequency decreases.
E) There is no change in the frequency.

Question

Quizplus · Accepted Answer

The resonant frequency of a mass-and-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. Increasing $k$ increases the value under the square root, thereby increasing the frequency.

Increasing the Spring Constant K of a Mass-And-Spring System Causes