A body executes shm under the influence of one force and has a period seconds and the same body executes shm with period seconds when under the influence of another force. When both forces act simultaneously and in the same direction, then the time period of the same body (in seconds) is:
Answers
Answer:
Under the force{ F }_{ 1 }F
1
time oscillation of the body { T }_{ 1 }T
1
{ F }_{ 1 }=M{ (\dfrac { 2\pi }{ T_{ 1 } } ) }^{ 2 }V;\quad where\quad M\quad is\quad the\quad mass\quad and\quad v\quad is\quad the\quad velocity\\ and\quad \\ { F }_{ 2 }=M{ (\dfrac { 2\pi }{ T_{ 2 } } ) }^{ 2 }VF
1
=M(
T
1
2π
)
2
V;whereMisthemassandvisthevelocity
and
F
2
=M(
T
2
2π
)
2
V
{ F }_{ Net }={ F }_{ 1 }+{ F }_{ 2 }\\ M{ (\frac { 2\pi }{ T } ) }^{ 2 }=M{ (\frac { 2\pi }{ { T }_{ 1 } } ) }^{ 2 }+M{ (\frac { 2\pi }{ { T }_{ 2 } } ) }^{ 2 }\\ \dfrac { 1 }{ { T }^{ 2 } } =\dfrac { 1 }{ { { T } }_{ 1 }^{ 2 } } +\dfrac { 1 }{ { { { T } }_{ 2 } }^{ 2 } } =\dfrac { { T }_{ 1 }^{ 2 }+{ T }_{ 2 }^{ 2 } }{ { T }_{ 1 }^{ 2 }{ T }_{ 2 }^{ 2 } } =\dfrac { { T }_{ 1 }{ T }_{ 2 } }{ \sqrt { { T }_{ 1 }^{ 2 }+{ T }_{ 2 }^{ 2 } } }F
Net
=F
1
+F
2
M(
T
2π
)
2
=M(
T
1
2π
)
2
+M(
T
2
2π
)
2
T
2
1
=
T
1
2
1
+
T
2
2
1
=
T
1
2
T
2
2
T
1
2
+T
2
2
=
T
1
2
+T
2
2
T
1
T
2