I Why does mechanical energy of a damped oscillator not vary with spring constant?

[MenchiKatsu]

I mean its part of the equation. 1/2 x k x xm x e^-bt/m for mechanical energy

 

[Dale]

The mechanical energy of a damped oscillator does depend on the spring constant. What makes you think it doesn’t?

 

[kuruman]

I mean its part of the equation. 1/2 x k x xm x e^-bt/m for mechanical energy

What equation? I see no such thing.

 

[MenchiKatsu]

Here are three sets of values for the spring constant, damping constant, and mass for the damped oscillator of Fig. 15-16. Rank the sets according to the time re-quired for the mechanical energy to decrease to one-fourth of its initial value, greatest first.
This is from halliday and resnick chapter 15. Checkpoint 6. The answer says it doesn't depend on spring constant.

 

[hutchphd]

Note that they carefully ask about the percentage change of energy over time. They are not saying, as you claim thay are, that

"mechanical energy of a damped oscillator not vary with spring constant"​

 

[kuruman]

Here are three sets of values for the spring constant, damping constant, and mass for the damped oscillator of Fig. 15-16.

Where are they? What does Fig. 15-16 show?

 

[MenchiKatsu]

Here it is

 

[fanofakirakurosawa]

Rate of decay (λ) depends on the b/m relation. You are confused about the value of the initial energy, which is:

and the equation of energy in terms of time t:

edit: deleted some part of the reply due I provided the entire solution