Please help with Part C i got 6.5% and it was wrong! Thank you! A gong makes a l

Question

Please help with Part C i got 6.5% and it was wrong! Thank you!

A gong makes a loud noise when struck. The noise gradually gets less and less loud until it fades below the sensitivity of the human ear. The simplest model of how the gong produces the sound we hear treats the gong as a damped harmonic oscillator. The tone we hear is related to the frequency f of the oscillation, and its loudness is proportional to the energy of the oscillation. If the loudness drops to 80% of its original value in 5.0 s, what is the time constant of the damped oscillation? Express your answer with the appropriate units. How long does it take for the sound to be 20% as loud as it was at the start? Express your answer with the appropriate units. What fraction of the original loudness remains after 1.0 min?

Explanation / Answer

We get =22s

And t=36s

Then

Partc)

The fraction of original loudness remains after 1 min is

We know that E(t)=E0 e(-t/)

Here t=1min=60s

E1min/E0=e(-60/22)

=0.06

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