Question

The amplitude of a damped harmonic oscillator becomes half of its initial value in 150 seconds find q factor. ​

Answer 1

Answer:

Amplitude of damped oscillator

A=A

0

e

−λt

;λ=constant,t=time

For t=1 min.

2

A

0

=A

0

e

−λt

⇒e

λ

=2

For t=3 min. A=A

0

e

−λ×3

=

(e

λ

)

3

A

0

=

2

3

A

0

⇒X=2

3

Answer 2

Given,

Final amplitude = $\frac{1}{2}$ (Initial amplitude)

Time = 150 seconds

To find,

The q-factor

Solution,

The q - factor is 6.28.

We may easily answer this numerical problem by following the steps below.

We know that,

Q-factor is pie times the ratio of original amplitude and the change in amplitude.

Here,

Let us assume the original amplitude to be A.

We know that,

The final amplitude becomes half times the initial amplitude.

Thus,

Final amplitude = $\frac{A}{2}$

Now,

Q- factor = $\frac{(pie) A}{A-\frac{A}{2} }$

               = π x 2

Thus, the Q-factor is π x 2, which is 6.28.