# Energy lost in a lightly damped osciallator

1. Sep 1, 2008

### hemetite

Qn2

The amplitude of a lightly damped osciallator decreases by 3% during each cycle of oscillation. What fraction of the energy is lost in each cycle?

Okay..i couldnt find anything about energy in the damped oscillation is my textbook..

but in SHM sections. it showed that

Energy of the SHM system = (1/2)kAsquare

where A is the amplitude and k is the coefficient for the spring..

but for lightly damped osciallator...the Energy of the SHM will change for every cycle..in this case, it will drop by 3%...

i know that the period for every cycle is the same but only the amplitude will change.

here is my guess...

Energy of the SHM system = (1/2)kAsquare -----------> first cycle

Energy of the SHM system = (1/2)k(A*0.97)square -----------> second cycle

Energy lost = (1/2)kAsquare - (1/2)k(A*0.97)square ----------> difference

Fraction of energy lost = difference/(1/2)kAsquare

am i right here?...i am a feeling i am wrong..but dun know how to aprroach this..

2. Sep 1, 2008

### tiny-tim

Hi hemetite!

(have a squared: ² )

I haven't checked whether your formula (1/2)kA² is right, but assuming it is …

yes, that's fine! (though a bit long-winded ) … now divide everything by (1/2)kA², and the result is … ?

3. Sep 1, 2008

### hemetite

..well...i am new here...i worry if i never explained thouroughly...you guys wont help me...hahaha...

anyway...here goes

=[(1/2)kA² - (1/2)k(0.97A)²] / [(1/2)kA²]

= 0.0591

should be correct now...

4. Sep 1, 2008

Sure is!

5. Sep 1, 2008

### hemetite

hahaha....man ..i love this forum..

people here are helpful and funny...

6. Sep 1, 2008

### tiny-tim

oi!
so are the fish!