A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-
mass damped oscillator having damping constant 'b', the correct equivalence would be:
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11th
Physics
Oscillations
Free, Forced and Damped Oscillations
A LCR circuit behaves like ...
PHYSICS
A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence would be :
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ANSWER
For a spring-mass damped oscillator
dt
2
d
2
x
+(
2
mk
2x
m
k
)
dt
dx
+(
m
k
)
2
x=0
⇒
dt
2
d
2
x
+2τw
0
dt
dx
+w
0
2
x=0
τ=
2
mk
c
⇒ damping ratio c=b⇒ damping constant
W
0
=
m
k
⇒ angular frequency
⇒
dt
2
d
2
x
+(
m
b
)
dt
dx
+(
m
k
)x=0
..........(1)
For LCR circuit
use KVL:-
V−L
dt
dI
−IR−
c
q
=0
⇒
dt
2
d
2
q
+
L
R
dt
dq
+(
LC
1
)q=
L
V
...........(2) I=
dt
dq
By comparing (1) and (2):=
L→m, R→b, LC→
k
m
⇒C→
k
1
option (D) is correct.
solution .
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