The selection process of a spring requires consideration of many elements. One essential element to note is the resonant frequency of the spring, also known as the natural frequency at which a spring oscillates. This article is designed to equip you with the knowledge on how to calculate this frequency accurately, enabling you to choose the right spring suitable for your design. Practical advice and safety instructions related to your design will be covered as well. For example, if your project is a clock, the resonant frequency of the spring must match the intended operational pace of the clock. Correct calculation and selection can optimally affect performance, while inaccuracies can lead to negative consequences.

Understanding Resonant Frequency in Springs

The resonant frequency of a spring is the frequency at which it naturally vibrates when it's not subjected to external factors like damping forces or loads. Calculating this frequency requires knowledge of the spring's rate, mass, and the conditions of its working environment.

The spring's rate indicates the amount of force needed to displace the spring by a certain distance, and it has a direct relationship with the resonant frequency. An increase in the force to compress or extend the spring coincides with an increase in the resonant frequency. For example, two springs, A and B, have spring rates of 10 N/m and 20 N/m respectively. Spring B, with a higher spring rate, will have a higher resonant frequency than spring A.

The mass of the spring inversely affects the resonant frequency. A spring with a heavier mass will have a lower resonant frequency, assuming all other parameters remain constant. Take for instance two springs, A and B, with identical spring rates but different masses of 5 g and 10 g respectively. Spring B, in this case, having a greater mass, will have a lower resonant frequency than spring A.

Other factors to consider include temperature and the presence of a damping medium in the environment. A higher temperature typically decreases a metallic spring's resonant frequency due to the rise in the metal's elasticity, pushing it to respond more slowly, thereby lowering the frequency. Similarly, damping media such as oil or gas can lower the resonant frequency by absorbing some of the kinetic energy, leading to a slower spring vibration rate.

When selecting a spring, ensure that the spring's resonant frequency does not coincide with the operational frequency of the application or any external load frequency. If these frequencies overlap, resonance amplification can occur, which could result in spring failure. In application, if a clock spring resonates at the same frequency as that generated by the clock's gears, this could lead to inaccurate timekeeping, or even potential spring damage.

Calculating and Selecting the Ideal Spring

The resonant frequency of a spring can be calculated by considering the mass supported by the spring and the spring rate. The spring rate, also known as the spring constant, refers to the force which must be applied to compress or extend the spring by a specific distance. If we consider a spring supporting a 2kg mass with a spring rate of 500 N/m, we can apply the formula f = 1/(2π√(m/k)), where m is the mass and k is the spring rate, to calculate an estimate of the resonant frequency. Using these parameters, the sample calculation becomes approximately 1/(2π√[(2kg)/(500 N/m)]), and the result is approximately 5.03 Hz. It's important to note that this formula assumes optimal conditions and does not consider the effects of external forces or dampening factors.

The resonant frequency of the spring chosen for a given application must not be the same as the operational frequency of the said application. This is essential to prevent destructive resonance, which can adversely affect the performance of the system or can cause spring failure. If, for example, the application operates at a consistent frequency of 10 Hz, the resonant frequency of the selected spring should be significantly different from this value to prevent undesired resonance effects. Therefore, in this context, a spring with a resonant frequency of 5.03 Hz would be inappropriate for an application with a steady operational frequency of 10 Hz.

Practical Tips and Precautions in Spring Selection


Selecting a spring with a suitable resonant frequency is crucial in engineering where both product performance and safety hinge on this factor. The spring's resonant frequency isn't an enigma, it can be measured with accuracy. This factor should not be overlooked during the selection process. Considering the spring's resonant frequency not just improves the longevity of your application, but also underscores the product's reliability.