A particle is executing shm if v1 and v2 are the speed of the particle and distance x1 and x2 from the equilibrium position show that the frequency of oscillations is f
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Answer:
Correct option is
D
2π
V
1
2
−V
2
2
x
2
2
−x
1
2
Using the expressions for velocity for SHM,
v
1
=ω
A
2
−x
1
2
v
2
=ω
A
2
−x
2
2
Squaring both,
v
1
2
=ω
2
(A
2
−x
1
2
) ....(3)
v
2
2
=ω
2
(A
2
−x
2
2
) ....(4)
Subtracting (4) from (3), v
1
2
−v
2
2
=ω
2
(x
2
2
−x
1
2
)
⇒4π
2
(x
2
2
−x
1
2
)=T
2
(v
1
2
−v
2
2
)
⇒T=2π
v
1
2
−v
2
2
x
2
2
−x
1
2
where we have used ω=
T
2π
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