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JEE Advanced 2015 Paper 1
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© examsnet.com
Question : 12
Total: 60
Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies
ω
1
and
ω
2
and have total energies
E
1
and
respectively.The variation of their momenta p with position x are shown in figure.If
a
b
=
n
2
and
a
R
=
n
.then the correct equation(s) is (are )
E
1
ω
1
=
E
2
ω
2
ω
2
ω
1
=
n
2
ω
1
ω
2
=
n
2
E
1
ω
1
=
E
2
ω
2
Validate
Solution:
For first oscillator
E
1
=
1
2
m
ω
1
2
a
2
a
n
d
p
=
m
v
=
m
ω
1
a
=
b
⇒
a
b
=
1
m
ω
1
.....(i)
For second oscillator
E
2
=
1
2
m
ω
2
2
R
2
and
m
ω
2
=
1
......(ii)
(
a
b
)
−
ω
2
ω
1
=
n
2
E
1
ω
1
2
a
2
−
E
2
ω
2
2
R
2
⇒
E
1
ω
1
=
E
2
ω
2
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