Question regarding angular frequency of a SHM

In summary, the conversation discusses the relationship between maximum kinetic energy and angular frequency in an oscillating system. It is established that the angular frequency, ω, remains constant despite changes in the maximum KE, as long as the spring constant and mass remain the same. This is because ω is dependent on the spring constant and mass, which are both constant in this scenario. Therefore, changing the KE would result in a change in amplitude, but not in the angular frequency.
  • #1
Janiceleong26
276
4
1. Homework Statement

image.jpg

image.jpg

Homework Equations


KE=½m(ωa)2

The Attempt at a Solution


So first I did this:
2.4x10-3= ½ mω2(1.5x10-2)2
To find mω2=21.33
And substitute that into the KE eqn to find the new amplitude, which is 1.30x10-2
But I only did that because that was the only way I could think of.
My question is, why is ω constant despite changes in the max KE?
 
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  • #2
Janiceleong26 said:
1. Homework Statement

View attachment 98703
View attachment 98704

Homework Equations


KE=½m(ωa)2

The Attempt at a Solution


So first I did this:
2.4x10-3= ½ mω2(1.5x10-2)2
To find mω2=21.33
And substitute that into the KE eqn to find the new amplitude, which is 1.30x10-2
But I only did that because that was the only way I could think of.
My question is, why is ω constant despite changes in the max KE?
How does the max KE depend on ω and the amplitude?
 
  • #3
Linear velocity will change during the oscillation (x changes)
upload_2016-4-7_10-57-15.png


so the KE

upload_2016-4-7_10-59-52.png


will too:
upload_2016-4-7_10-58-50.png
 

Attachments

  • upload_2016-4-7_10-59-47.png
    upload_2016-4-7_10-59-47.png
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  • #4
ehild said:
How does the max KE depend on ω and the amplitude?
Max KE=½m(ωa)2
 
  • #5
@Physics-Tutor Thanks but I'm still confused. How do we know that the angular frequency, ω, is constant?
 
  • #6
Janiceleong26 said:
Max KE=½m(ωa)2
Changing KE means changing the amplitude if it is the same oscillator. You know that ω=√(k/m). If the spring is the same and the mass of the load is the same, why should the frequency change?
 
  • #7
Janiceleong26 said:
@Physics-Tutor Thanks but I'm still confused. How do we know that the angular frequency, ω, is constant?
We use the same spring and loading mass.
 
  • #8
Janiceleong26 said:
Thanks but I'm still confused. How do we know that the angular frequency, ω, is constant?
ehild said:
We use the same spring and loading mass.
ehild is correct:
upload_2016-4-7_14-11-33.png


k is the spring constant, m the mass. These two are constant, so the angular velocity is constant.
 

Attachments

  • upload_2016-4-7_14-12-10.png
    upload_2016-4-7_14-12-10.png
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  • upload_2016-4-7_14-12-13.png
    upload_2016-4-7_14-12-13.png
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  • upload_2016-4-7_14-12-27.png
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  • #9
ehild said:
Changing KE means changing the amplitude if it is the same oscillator. You know that ω=√(k/m). If the spring is the same and the mass of the load is the same, why should the frequency change?
Physics-Tutor said:
ehild is correct:
View attachment 98717

k is the spring constant, m the mass. These two are constant, so the angular velocity is constant.
Oh, I got it. Thanks a lot !
 

Related to Question regarding angular frequency of a SHM

What is the definition of angular frequency in SHM?

The angular frequency in SHM (Simple Harmonic Motion) is the rate at which a particle or object oscillates back and forth around its equilibrium point. It is denoted by the symbol ω (omega) and is measured in radians per second.

How is angular frequency related to period and frequency in SHM?

The angular frequency is directly proportional to the frequency and inversely proportional to the period in SHM. This means that as the angular frequency increases, the frequency also increases but the period decreases, and vice versa.

What is the formula for calculating angular frequency in SHM?

The formula for calculating angular frequency in SHM is ω = 2π/T, where ω is the angular frequency and T is the period of oscillation. Alternatively, it can also be calculated as ω = 2πf, where f is the frequency in Hertz (Hz).

How does angular frequency affect the amplitude of oscillation in SHM?

The angular frequency does not affect the amplitude of oscillation in SHM. The amplitude of oscillation is solely determined by the initial displacement of the object from its equilibrium point and the energy of the system.

Can angular frequency be negative in SHM?

Yes, angular frequency can be negative in SHM. This indicates that the object is oscillating in the opposite direction of the initial displacement. However, the magnitude of the angular frequency remains the same regardless of its sign.

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