- #1
hemetite
- 50
- 0
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 couldn't 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..
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 couldn't 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..
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