Question
Asked Dec 2, 2019
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A pendulum has its amplitude of oscillation decrease to 32.5% of its original value. If it takes 19.4 s for this to occur, what is the time constant for the pendulum?


- 8.63 s
- 34.5 s
- 2.79 s
- 17.3 s

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Expert Answer

Step 1

Given data:

At, t0 s
= A
At, t 19.4 s
32.5
x(19.4) A
100
0.675A
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At, t0 s = A At, t 19.4 s 32.5 x(19.4) A 100 0.675A

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Step 2

For damped pendulum:

x(t)x(0)e
0.675A Ae-t
0.675 e
-i/T
1
e
0.675
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x(t)x(0)e 0.675A Ae-t 0.675 e -i/T 1 e 0.675

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Step 3
Taking In both side:
1
t
= In
0.675
t
1
n
0.675
19.4
1
log
0.675
= 49.3585 s
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Image Transcriptionclose

Taking In both side: 1 t = In 0.675 t 1 n 0.675 19.4 1 log 0.675 = 49.3585 s

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