General procedure for finding stiffness in vibration problems

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To find stiffness in vibration problems, start by determining the force acting on the system when displaced from its equilibrium position. Analyze the specific configuration, such as a mass-spring system or a rigid body with attached springs. Use the relationship of stiffness defined as stiffness = force/displacement to calculate "k." Consider the effects of gravity and other forces relevant to the system's setup. This general approach can be applied to various single degree of freedom (SDOF) problems.
bda23
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Hi, I have forgotten quite a bit of my vibration studies, so I have a fairly basic question. Essentially, when you want to find the natural frequency of a single dof system, you use ω=√k/m. However, does anyone know a general procedure (not problem-specific) for finding "k" that is applicable to most SDOF problems. Examples would be something along the lines of a a rigid massless bar, hinged at one end, with a few springs attached and a mass at one end, or a rigid L-shaped bar hinged somewhere and gravity acting, or a water column in a U-shaped test tube (height vibrating with gravity)... I think you get the idea. Basically, I am looking for a series of steps that you would go through in all these situations in order to find the stiffness. Thanks.
 
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Stiffnesss = Force / displacement.

Work out the force on the system when it is moved a small distance from its equilibrium position.
 

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