Question regarding angular frequency of a SHM

[Janiceleong26]

1. Homework Statement

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?

 

[ehild]

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?

 

[Physics-Tutor]

Linear velocity will change during the oscillation (x changes)

so the KE

will too:

 

[Janiceleong26]

How does the max KE depend on ω and the amplitude?

Max KE=½m(ωa)²

 

[Janiceleong26]

@Physics-Tutor Thanks but I'm still confused. How do we know that the angular frequency, ω, is constant?

 

[ehild]

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?

 

[ehild]

@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.

 

[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.

ehild is correct:

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

 

[Janiceleong26]

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?

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 !