15.53:
a) See Exercise 15.10;
,
2
2
2
y
ω
a
t
y
y

=
=
∂
∂
and so
.
2
2
ω
xμ
mω
k
∆
=
∆
=
′
b)
(
29
2
2
2
2
2
4
2
2
μλ
F
π
λ
πv
πf
ω
=
=
=
and so
.
)
4
(
2
2
x
F
π
k
∆
λ
=
′
The effective force constant
k
′
is independent of amplitude, as
for a simple harmonic oscillator, and is proportional to the tension that provides the
restoring force. The factor of
2
1
λ
indicates that the curvature of the string creates the
restoring force on a segment of the string. More specifically, one factor of
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 Force, Mass, Simple Harmonic Oscillator

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