# What is Natural frequency: Definition and 130 Discussions

Natural frequency, also known as eigenfrequency, is the frequency at which a system tends to oscillate in the absence of any driving or damping force.The motion pattern of a system oscillating at its natural frequency is called the normal mode (if all parts of the system move sinusoidally with that same frequency).
If the oscillating system is driven by an external force at the frequency at which the amplitude of its motion is greatest (close to a natural frequency of the system), this frequency is called resonant frequency.

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1. ### Engineering Natural frequency of clamped-hinged column

I have a column clamped at the bottom and for the top, I use hinged BC but free at the Y axis. I have the dimension and the material properties. How to calculate its natural frequency?
2. ### Spring first natural frequency and hysteresis

Could anyone help me with some info on compression helical springs. First I would like to know if this type of spring would even have any appreciable histeresis when new, and if so does it does it grow with repeted use and age. I would also like to know if there is any relationship beteen the...
3. ### Engineering Finding the natural frequency of transfer function (2s) / (3s^2+5s+2)

In the context of control systems, if I have a vibratory second-order system, (ω_n)^2 / [s^2 + 2ζ(ω_n) + (ω_n)^2], I know how to get the natural frequency ω_n. So, if I have something like 2 / (3s^2+5s+2), I know how to get the natural frequency ω_n. However, if I instead have something like...
4. ### Measuring the natural frequency of a spring-mass system driving force

Hi, On a driving force graph ##y = displacement (m)## and ##x = time## where the external force start at t = 0 and the system is in equilibrium at x=0, it's easy to find the driving frequency. $$F = \frac{\omega}{2\pi}, \omega = \frac{2\pi}{T}$$ and we can get ##T## easily with the steady...
5. ### Effect of initial stress on the natural frequency of vibration

Hello all, We might have observed that by tightening a string of a musical instrument, the natural frequency of the string changes. But I can not describe this phenomenon by the theory of linear elasticity. Also if we simulate the vibration of a bar with the help of structural software tools...
6. ### B Mechanical Resonance and Natural Frequency at the Atomic/Lattice Level

How do we explain resonance of a complex system (say a bridge) at the atomic level? What's happening to its molecules when it's oscillating at resonance, and does that have anything to do with the frequency at which the molecules oscillate in the material?

9. ### I Find Practical Resonance Frequencies in Linear Differential Equations

Hi all, I would like to know what is the equation upon which I can use to determine the practical resonance frequencies in a system of second order, linear differential equations. First some definitions: What I mean by practical resonance frequencies, is the frequencies that a second order...
10. ### What is the governing equation of a spring with sinusoidal excitation?

Hi, Most of the spring vibration lectures assume spring to be fixed on one end and mass on the other end [Example]. In my case, spring has a sinusoidal excitation on one end and mass on other end. Pl. refer the image below. How to get the governing equation? With that I also want to find the...
11. ### How Do Resonant MEMS Accelerometers Detect Changes in Acceleration?

Hello, Suppose that I have a resonant MEMS accelerometer. It has a suspending beam (resonator) and I want to apply an AC voltage to the beam which will be at beam's resonant(natural) frequency. When I do this, I will create a standing wave pattern of acoustic waves (vibrations) inside the...
12. ### A Natural frequencies of simplified tympanic membrane model

I am trying to anallytically determine natural frequencies ƒ of the tympanic membrane. I am using 2D sectorial annulus membrane as a simplified model of tympanic membrane according to following picture The parameters that i want to use are following: THICKNESS = 0,1 mm The natural...
13. ### Standing Wave Fundamental Frequency and Particle Vibration

For a wave A sin ( kx - ωt) and a wave A sin ( kx + ωt) traveling opposite to each other, on evaluating by applying superposition principle , the resultant displacement function is 2A sin ( kx ) cos (ωt) . For different Node Anti-node configurations we calculate natural frequencies of the...
14. ### Probability at a temperature T that a system has a particular energy

Salutations, I'm starting in statistical mechanics and reviewing some related studying cases I would like to understand what occurs in small systems with normal modes of vibration, for example, a small system that has 2 normal modes of vibration, with natural frequencies $$\omega_1$$ and...
15. ### How to calculate natural frequency of timing belt

Hello I am designing a shaft and it will be powered via belt pulley system. The ideal RPM of the shaft is 8000 RPM. How do I calculate the natural frequency of the timing belt to ensure resonance is never met? From what I read online it has to do with belt pretension, but even then I am little...
16. ### Natural frequency in stationary and rotating frames....

Hi, I am trying to gain insight into using stationary vs. rotating coordinate frames for natural frequency calculations. I have seen many FE codes suggest that critical frequencies can be calculated differently in rotating and inertial frames, so i wanted to do a 1D calc to see for myself how...
17. ### Natural Frequency of a Foam Block?

Hello everyone, Looking for some help on how to go about finding the natural frequency of a block of foam. The foam has a density of 0.37 lbs./ft^3 and is 48"x48"x8" (LxWxD) in size. Weight is approximately 5.4 lbs. I have been digging around the internet for quite some time with no such luck...
18. N

### Natural Frequency of Elastic Pipe with Different Pressures

Hi, I have a 3mm diameter flexible silicone tube with wall diameter of 0.5mm. If this tube is filled with water at different pressures, how does the internal pressure present itself during modal testing (either shaker or impact testing). The tube lies on rigid table so it is completely...
19. ### First natural frequency for bending, axial and torsion modes

Homework Statement We have a rod of length L fixed to a rigid support. At the end of the rod there is a mass, m. Assume that the rod has no mass. Find the first natural frequency for the bending, axial and torsion modes. Homework EquationsThe Attempt at a Solution So I'm reviewing some stuff...
20. ### Why am I not getting the correct natural frequency?

Homework Statement To find the natural frequency of a uniform cantilever beam, the area moment of inertia, cross-sectional area and density are not given, everything else is given by the lab, our group got a theoretical natural frequency( it might be angular frequency) of 27.44 Hz from lab's...
21. ### What is meant by natural frequency?

An object only undergoes an oscillation when I act on it. If I push a spring, it will have a certain frequency, and if I push a different way, it will have a different one. What is meant by natural frequency? What is meant by resonance?
22. H

### Natural Frequency of a rod

does the natural frequency of a steel rod rigidly fixed will vary when it is assembled with another rod by universal joint?
23. ### Natural frequency of pulley system

Homework Statement https://www.physicsforums.com/attachments/197474 Homework Equations 3. The Attempt at a Solution [/B] ma + kx = 0 I know how to do it if the spring is in the middle of the pulley, not using energy method. by the free body diagram. But I am stuck at this. [Updated: I know...
24. ### Natural Frequency for torsional vibration

I am trying to calculate natural frequency for torsional vibration of fixed fixed beam using following formula. =1/2*3.142 sqrt(K*g/mr^2) hz Where K=J*G/L and G=Modulus of rigidity g=acceleration due to gravity=386.4 in/se2 m=mass hanging on the beam at distance 'r' from the longitudenal...
25. ### Determine the natural frequency

Homework Statement Determine the natural frequency in Hz of the system sketched below given the following values: Mass m=4kg Spring stiffness k=28kN/m Length a=121mm Length b=93mm Homework Equations ω=(k/m)^0.5 The Attempt at a Solution so probably I need to find m should I multiply...
26. ### Natural frequency of an Oscillating water column device

Homework Statement Assuming that an OWC device is floating/moored in monochromatic waves. When there isn't air pressure distribution inside (atmospheric condition) the device behaves as an undambed body (with the oscillating chamber open to the atmosphere). When there is air pressure...
27. ### Automotive Mode shapes of half-rhombus mechanism

I want to determine the natural frequencies and the mode shapes of the given mechanism ( it consists of 2 inclined beams connected together by a compliant link, the bottom end is fixed and the upper end is a roller support). I have done Finite element modeling but I need to get some analytical...
28. ### Determine the natural frequencies experimentally

How can we determine the system properties (natural frequencies & damping ratio ) practically using forced vibration? One way is to measure the phase angle, using the bode plot, the exciting frequency corresponding to 90 (deg) phase shift should be the natural frequency, are there any other...
29. ### I with the free vibration of bar problem

Homework Statement Find the free vibration of the bar supported by a spring and a viscous damper (See attached figure) Homework Equations (a)Derive the equation of motion (b) Obtain the moment of inertia of bar (c) obtain natural frequency when d=0. The Attempt at a Solution
30. ### Natural Frequency & damping coefficient from transfer function

Homework Statement Here is the transfer function of a buck converter I derived: What I need to do next is obtain equations for w0 and ζ. I know how to do this for equations that follow the general form: But in this case I just can't figure out exactly how to do it. How do I find a...
31. ### Where does natural frequency comes from?

I know everything has a natural frequency that is a intrinsic property to the body in question. For example, a string vibrating has the largest amplitudes when it's vibrating near it's natural frequency, and the same thing happens with other things too (like the Tacoma Bridge). Natural...
32. ### Natural frequency of a mass spring system

Homework Statement Homework Equations T = 2π√(m/k) mx'' + kx = 0 F = ma The Attempt at a Solution I don't honestly know where to start with this. I'm really out of my league in this class, and I'm trying my best to catch up with the things I didn't quite master in Dynamics and Physics... As...
33. ### Boundary conditions of that beam.

Hi all! I have to calculate the natural frequency of the system. Any idea of boundary conditions of this case? There is beam supported by two springs on the left side.
34. ### Determination of the natural frequency of a Hartnell governor

Homework Statement Homework EquationsThe Attempt at a Solution I found this solution for the nature frequency but here it does not include the Ball weight and centrifugal force in the moment balance equation about the pivot (O), it is wrong answer...is not it? I tried to solve the problem...
35. ### How to find the natural frequency in ansys apdl

Hi! I am new in ansys. I am doing rotor dynamic study of a high speed rotating shaft. the shaft comprise of two discs and at the it ends the shaft is supported by the bearing I am facing problem in modelling stage please tell me how to model the bearing and disc briefly.I am uploading the image...
36. ### Sketch output response of system

Homework Statement Sketch output respons of system who have a input is a unit step (Amplitude of the system = 1)Homework Equations · Damping factor = 0,5 · Gain factor = 2 · Natural angular frequency = 4 Rad/sThe Attempt at a SolutionI have: 1. Draw a step respons in a x-y axis 2. And...
37. ### Damped vs Undamped Driven Springs and superposition?

Modeling driven undamped spring systems in my diff eqs text at the moment. So I've just worked through the derivation of x(t) = C\cos{(\omega_0t - \alpha)} + \frac{F_0/m}{\omega_0^2-\omega^2}\cos{\omega t} And it's clear that this describes the superposition of two different oscillations...
38. ### System Analysis - Determining Dampening and Natural Frequency

Homework Statement Problem and work attached. It is mostly diagrams so I have just uploaded the pictures. I think what I did to determine the transfer function was correct. I'm not quite sure how to do the last section of part (a) where I need to determine the dampening, static gain, and...
39. ### Error in Natural Frequency (Lab)

So I just did a lab on resonant frequency, and have to find the error of the period: $$T = 2π\sqrt{m/k}$$ m and k were measured with an error of Δm and Δk. My teacher didn't explain well how to do errors, so I just want to know if I did this right. Prorogation of Error equations: y=x^n ⇒...
40. ### Natural Frequency: Find Equation of Motion

Homework Statement Find the natural frequency Homework Equations On picture The Attempt at a Solution Just need help with the equation of motion.
41. ### Natural frequency of a simple harmonic system

Homework Statement Derive the natural frequency f_n of the system composed of two homogeneous circular cylinders, each of mass M, and the connecting link \text{AB} of mass m. Assume small oscillations. Homework Equations The sum of the kinetic + potential energies in an isolated system...
42. ### Natural Frequencies and Vibration Amplitudes of Object A

Suppose a sound wave with multiple natural frequencies--a complex sound wave--strikes Object A. Some of those frequencies matches the natural frequencies of Object A. A) Will Object A vibrate at all the different frequencies or only to its natural frequencies? B) If Object A vibrates at all...
43. ### Why natural frequency conveyors are not dangerous?

I've read that natural frequency conveyors are very efficient because the drive only compensates for the amplitude that's lost in the elastic supports. Could you please explain how is this different from working at resonant frequency which is so dangerous? P.S. What kind of analysis should I...
44. ### What are the features of natural frequency vibro-conveyor?

I'm considering two types of vibrating feeders, brute force and natural frequency. Can you tell me how natural frequency conveyor works? What kind of design should I choose to transfer light materials? What If I want to use an upwards angle, how do I determine that upward going path of...
45. ### Finding the undamped natural frequency of 2nd order system

the following 2nd order differential equation is given: 2y'' + 4y' +8y=8x........(1) i want to find damping ratio, undamped natural frequency, damping ratio coefficient and time constant for the above system. solution: comparimg (1) with general system equaion (veriable can be exchanged)...
46. ### How to calculate natural frequency of a circular plate

I am trying to get used to using a Data Physics analyzer at work in order to measure the natural frequency of components of a larger project I am involved in, my method described is intentionally crude as I was trying to do this as a quick play around before diving into the real thing.. To...
47. ### Natural frequency of 3 coulomb force bound particles in EF

Homework Statement I was given a task to model (using Matlab) 3 identical particles in external field and find spectra of lowest system energy states using gradient descend method for each particle in the system. I did a run of 500 random generated coordinates and found this distribution...
48. ### Find total length of cylinder (springs, natural frequency)

Homework Statement A simple pressure relief device is shown in Figure Q6.1 below. It consists of a piston of mass 0.5 kg and thickness 3 cm sliding without leakage or friction into a cylinder of diameter 5 cm. The bottom section of the cylinder can be exposed to a varying source of pressure...
49. ### MHB Natural frequency of a crane dropping a car

An electromagnet weighing $$3000$$ lb is at rest while holding an automobile of weight $$2000$$ lb in a junkyard. The electric current is turned off, and the automobile is dropped. Assuming that the crane and the supporting cable have an equivalent spring constant of $$10000$$ lb/in, find the...
50. ### MHB Natural frequency of a pendulum being lowered at 2m/s

A heavy machine weighing $$9810$$ N is being lowered vertically down by a winch at a uniform velocity of $$2$$ m/s. The steel cable supporting the machine has a diameter of $$0.01$$ m. The winch is suddenly stopped when the steel cable's length is $$20$$ m. Find the period and amplitude of the...