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F
a
+
F
y
=
0
{\displaystyle F_{a}+F_{y}=0}
F
a
=
−
F
y
{\displaystyle F_{a}=-F_{y}}
m
a
=
−
k
y
{\displaystyle ma=-ky}
a
=
−
k
m
y
{\displaystyle a=-{\frac {k}{m}}y}
d
2
d
t
2
y
(
t
)
=
−
k
m
y
(
t
)
{\displaystyle {\frac {d^{2}}{dt^{2}}}y(t)=-{\frac {k}{m}}y(t)}
y
(
t
)
=
A
sin
ω
t
{\displaystyle y(t)=A\sin \omega t}
ω
=
k
m
{\displaystyle \omega ={\sqrt {\frac {k}{m}}}}