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Physics
Physics
Problem
Show that for a particle executing SHM described by
x
(
t
)
=
A
cos
(
ω
t
+
ϕ
)
x(t)=A\cos(\omega t+\phi)
x
(
t
)
=
A
cos
(
ω
t
+
ϕ
)
, the kinetic energy as a function of time can be written as
K
(
t
)
=
1
2
m
ω
2
A
2
sin
2
(
ω
t
+
ϕ
)
K(t)=\tfrac12 m\omega^{2}A^{2}\sin^{2}(\omega t+\phi)
K
(
t
)
=
2
1
m
ω
2
A
2
sin
2
(
ω
t
+
ϕ
)
.
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