Time period and natural frequency

In summary, the terminologies natural time period and frequency are typically used for simple harmonic motions and not for periodic/sinusoidal motions. The natural frequency refers to the frequency of the fundamental mode which is always simple harmonic. Natural frequency and time period can be used for motions with periodicity if there is a clear reason for why that frequency or period is more natural. For example, the simple harmonic oscillator and vibrating string have natural frequencies determined by physical parameters, while the rotating Earth does not have a distinct reason for its rotation frequency.
  • #1
svishal03
129
1
A fundamnetal question here;

IS it that the terminologies natural time period and frequency are used only for simple harmonic motions and not for motions which are periodic/sinusoidal like an SHM?
 
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  • #2
svishal03 said:
A fundamnetal question here;

IS it that the terminologies natural time period and frequency are used only for simple harmonic motions and not for motions which are periodic/sinusoidal like an SHM?
Usually, natural frequency refers to the frequency of the fundamental mode.

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/reson.html#c3
 
  • #3
And when we say fundamental mode, it is always simple harmonic, right?

Am I right natural frequency and time period can be used for motions which have a periodicity?
 
  • #4
Not just a periodicity but some clear reason why that frequency or period is more natural than any other. For example, the simple harmonic oscillator has a natural frequency which is determined by the ratio of spring constant to mass. Similarly a vibrating string has a fundamental frequency determined by the density, spring constant, and length.

The rotating Earth on the other hand is more or less periodic but there is no overwhelming reason why it wants to rotate at 1 cycle/day as opposed to any other frequency.
 
  • #5


That is correct, the terms "natural time period" and "natural frequency" are typically used in the context of simple harmonic motion (SHM). This is because SHM is a specific type of periodic or sinusoidal motion that follows a precise mathematical relationship between displacement and time. Therefore, the natural time period and frequency can be easily calculated for an SHM system.

However, these terms can also be used in other periodic or sinusoidal motions, as long as they follow a similar mathematical relationship. For example, in a spring-mass system undergoing damped harmonic motion, the natural frequency can still be calculated using the same equation as in SHM.

So while these terms are most commonly associated with SHM, they can also be applied to other periodic or sinusoidal motions as long as they follow the same principles. I hope this helps clarify any confusion.
 

1. What is the relationship between time period and natural frequency?

The time period and natural frequency are inversely proportional. This means that as the time period increases, the natural frequency decreases and vice versa.

2. How do you calculate the natural frequency of a system?

The natural frequency of a system can be calculated by taking the square root of the stiffness divided by the mass of the system. It is often represented by the symbol "ω" and measured in units of radians per second.

3. What factors affect the time period and natural frequency of a system?

The time period and natural frequency of a system are affected by the mass, stiffness, and damping of the system. A higher mass or stiffness will result in a longer time period and lower natural frequency, while higher damping will decrease both the time period and natural frequency.

4. How does the natural frequency impact the behavior of a system?

The natural frequency is a characteristic property of a system and determines how it will respond to external forces or vibrations. When an external force is applied at the natural frequency of a system, it will experience resonance and amplify the vibrations. This can lead to damage or failure of the system if not properly controlled.

5. Can the time period and natural frequency of a system be changed?

Yes, the time period and natural frequency of a system can be changed by altering the mass, stiffness, or damping of the system. This can be achieved through design modifications or by applying external forces to the system.

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