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IIT JEE Advanced 2011 Paper 1
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© examsnet.com
Question : 16
Total: 69
Consider the spring–mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is
Validate
Solution:
We have
E =
P
2
2
m
+
1
2
k
x
2
However, E =
1
2
k
a
(
t
)
2
, where A(t) is amplitude. Therefore,
1
2
k
A
(
t
)
2
=
P
2
2
m
+
1
2
k
x
2
or
p
2
+
m
k
x
2
=
m
k
A
(
t
)
2
The equation of motion is a circle in phase space whose radius is decreasing due to the friction of the liquid.
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