To find the natural frequency of a spring-mass system, you need to know the mass of the object attached to the spring (m) and the spring constant (k) of the spring itself. The natural frequency (f) can be calculated using the following formula:
f = 1 / (2π) * √(k / m)
In this formula, π represents the mathematical constant pi (approximately 3.14159). The square root (√) of the ratio between the spring constant (k) and the mass (m) determines the angular frequency (ω). Dividing ω by 2π gives you the natural frequency (f) in units of cycles per second, or Hertz (Hz).
It's important to ensure that the mass and spring constant are in consistent units. For example, if the mass is in kilograms (kg), the spring constant should be in Newtons per meter (N/m) for the formula to work correctly.
Keep in mind that this formula assumes an idealized, simple harmonic motion of the spring-mass system, where there are no other forces or damping present. In real-world situations, there may be additional factors to consider that can affect the system's behavior.