What gives rise to natural frequency?

[audreyh]

What gives rise to natural frequency? Resonance is when an oscillating force has a frequency that matches the natural frequency of a system... but what gives rise to the natural frequency of the system?

 

[jtbell]

That depends on the system. For a mass on a spring, the natural frequency depends on the mass and the spring constant (stiffness of the spring). For an oscillating electrical circuit, the natural frequency depends on the inductance and capacitance. Etc.

 

[audreyh]

That depends on the system. For a mass on a spring, the natural frequency depends on the mass and the spring constant (stiffness of the spring). For an oscillating electrical circuit, the natural frequency depends on the inductance and capacitance. Etc.

Thanks for the reply! So how about for a complicated system like a guitar string, or the Tacoma Narrows bridge, or a wine glass with water in it.

Also, do you know of a textbook that covers the mathematical formulation of showing the natural frequency? Would it be in Marion and Thorton's classical mechanics book?

 

[f95toli]

Calculating the mechanical resonance frequencies (note the plural, real object always have MANY resonance frequencies, if you count the harmonics infinitely many) for an object is easy in principle but can be extremely complicated for object such as a bridge; in most cases you need numerical simulations.
However, the basic idea is simply to solve the wave equation for that object: the "in" parameters being the speed of sound and the geometry.

But again, the math is quite complicated since the wave equation is a partial differential equation (albeit a simple one); even simple shapes such as a disc require university level math (usually covered in courses in Fourier analysis).