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A particle performs SHM on x- axis with ...

A particle performs `SHM` on x- axis with amplitude `A ` and time period period `T` .The time taken by the particle to travel a distance `A//5` string from rest is

A

`(T)/(20)`

B

`T/(2pi) cos^(-1)(4/5)`

C

`T/(2pi)cos^(-1)(1/5)`

D

`T/(2pi)sin^(-1)(1/5)`

Text Solution

Verified by Experts

The correct Answer is:
B
Particle is starting from rest, i.e. from one of its extreme position. As particle moves a distance `A/5`, we can represent it on a circle as shown.
`cos theta=(4A)/(5)=4/5 " " theta=cos^(-1)(4/5)`
`omegat=cos^(-1)(4/5) " " t=1/(omega) cos^(-1)(4/5)`
`=T/(2pi) cos^(-1)(4/5) `
As starts from rest, i.e. from extreme position `x=A sin (omegat+phi)`
At t=0 ,x=A `rArr phi=(pi)/2 " " :. A-A/5=A cos omegat`
`4/5=cos omega t " " rArr omega t=cos^(-1)(4/5) rArr " " t=T/(2pi) cos^(-1)(4/5)`
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Knowledge Check

  • A particle performs SHM on x- axis with amplitude A and rtime period period T .The time taken by the perticle to travel a distance A//5 string from rest is

    A
    `(T)/(20)`
    B
    `(T)/(2 pi) cos^(-1)((4)/(5))`
    C
    `(T)/(2 pi) cos^(-1)((1)/(5))`
    D
    `(T)/(2 pi) sin^(-1)((1)/(5))`

  • A particle is performing SHM along x-axis with amplitude 6.0 cm and time period 12 s. What is the minimum time taken by the particle to move from x=+3cm to x=+6cm and back again?

    A
    1 s
    B
    2 s
    C
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    A
    `0.6 sec`
    B
    `0.4 sec`
    C
    `0.3 sec`
    D
    `0.2 sec`

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