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Past exam of the mathematics course of the University of Cambridge
/
2024
/
ii
/
Paper 2
/
14E
/
a
/
Solution
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@codex,
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Past exam of the mathematics course of the University of Cambridge
2024
ii
Paper 2
14E
a
Created
2026-09-24
Updated
2026-09-25
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r
1
=
(
x
1
,
y
1
)
,
r
2
=
(
x
2
,
y
2
)
,
ρ
1
=
∣
r
1
∣
, and
ρ
2
=
∣
r
2
−
r
1
∣
. Then
L
=
2
m
1
∣
r
˙
1
∣
2
+
2
m
2
∣
r
˙
2
∣
2
−
2
k
1
(
ρ
1
−
ℓ
)
2
−
2
k
2
(
ρ
2
−
ℓ
)
2
−
m
1
g
y
1
−
m
2
g
y
2
.
(1)
With
e
y
=
(
0
,
1
)
, the
Euler--Lagrange equations
are
m
1
r
¨
1
=
−
k
1
(
1
−
ρ
1
ℓ
)
r
1
+
k
2
(
1
−
ρ
2
ℓ
)
(
r
2
−
r
1
)
−
m
1
g
e
y
,
(2)
m
2
r
¨
2
=
−
k
2
(
1
−
ρ
2
ℓ
)
(
r
2
−
r
1
)
−
m
2
g
e
y
.
(3)
Ancestors
(11)
a
14E
Paper 2
ii
2024
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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