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951.

Whatis the displacement equation of S.H.M. with an amplitude 2m , if 120 oscillations are performed during one minute and initial phase is `60^(@)` [ Consider displacement time equation of the form `y = A sin( omega t + phi)]` ?A. `2 sin (4pi t + (pi)/(3))`B. ` 2 sin ( 4 pi t )`C. ` 2 sin ( 2pit (pi)/(3))`D. ` 2 sin ( pit + (pi)/(3))`

Answer» Correct Answer - 1
Discussion
952.

A vibratory motion is represented by `x=2Acosomegat+Acos(omegat+(pi)/(2))+Acos(omegat+pi)+(A)/(2)cos(omegat+(3pi)/(2))`. the resultant amplitude of the motion isA. `(9A)/(2)`B. `(sqrt(5)A)/(2)`C. `(5A)/(2)`D. 2A

Answer» Correct Answer - B
`x=2Acosomegat+Acos(omegat+(pi)/(2))+Acos(omegat+pi)+(A)/(2)cos(omegat+(3pi)/(2))`
`=2Acosomegat-Asinomegat-Acosomegat+(A)/(2)sinomegat`
`=Acosomegat-(A)/(2)sinomegat`
`therefore`The amplitude of the resultant motion is
`A_(R)=sqrt((A)^(2)+(-(A)/(2))^(2))=(sqrt(5)A)/(2)`
Discussion
953.

A particle moves along x-axis according to relation `x= 1+2 sin omegat`. The amplitude of S.H.M. isA. 2B. 1C. `sqrt(5)`D. 3

Answer» Correct Answer - 1
Discussion
954.

A particle moves on y-axis according to the equation `y = A +B sin omegat`. Amplitude of motion isA. `A`B. `B`C. `sqrt(A^(2)+B^(2))`D. `A -B`

Answer» Correct Answer - B
Discussion
955.

If ` y=alpha cos omega t+b sin omegat`, show that it represents SHM. Determine its amplitude.A. 6 unitsB. 8 unitsC. 10 unitsD. 14 untis

Answer» Correct Answer - 3
Discussion
956.

The particle is moving such that its displacement along x-axis as a function of time is given by `x(x -6) = 1 - 10 cos omegat`. Find amplitude, time period and mean position.

Answer» `x(x-6) = 1 -10 cos omegat` By adding `9` on both sides
`x^(2) -6x +9 = 10 - 10 cos omegat`
`(x-3)^(2) = 10 [1-cos omegat] =5[sin^(2) ((omegat)/(2))]`
`(x-3) = sqrt(5) sin ((omegat)/(2))`
So motion of particle is `SHM` with `A = sqrt(5)` units,
`T = (4pi)/(omega)` units & means position is at `x = 3` units.
Discussion