Question

Calculate the natural frequency of a spring-mass system?

Answer 1

Explanation:

1. The spring-mass system (commonly known in classical mechanics as the harmonic oscillator) is one of the simplest systems.
2. In order to calculate the natural frequency, since it has only one moving object in only one direction (technical term “single degree of freedom system”) which is the mass $M$, and it is only affected by one external force that is “Tension or compression in the spring”.

To calculate the natural frequency of a spring-mass system. When calculating the natural frequency, we use the following formula

$f=\frac{\omega }{2\pi }$

Here, the $\omega$ is the angular frequency of the oscillation that we measure in radians or seconds. We define the angular frequency formula:

$\omega =\sqrt{\frac{k}{M}}$

Therefore, from the above two equations, the formula for natural frequency becomes

$f=\frac{1}{2\pi }\sqrt{\frac{k}{M}}$

$f$ is the natural frequency, $k$ is the spring constant for the spring or the stiffness of the spring, $M$ is the mass of the ball.