the amplitude of an oscillator of frequency 200 hz falls to 1/10 to its initial value after 2000 cycles. find its initial amplitude
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Its is a damped oscillation, where amplitude of oscillation at time t is given by A=a
0
e
−γt
where a
0
= initial amplitude of oscillation
γ= damping constant
As per question,
3
a
0
=a
0
e
−γ100/v
...(i)
(where v is the frequency of oscillation)
and A=a
0
e
−γ200/v
...(ii)
From (i);
3
a
0
=a
0
e
−γ×100/v
...(iii)
Dividing equation (ii) by (iii), we have
a
0
(1/3)
A
=
e
−γ×100/v
e
−γ×200/v
=e
−γ×100/v
=
3
1
or A=a
0
×
3
1
×
3
1
=
9
1
a
0
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