Home
Class 11
PHYSICS
A particle is subjected to two SHMs x(1)...

A particle is subjected to two `SHMs x_(1) = A_(1) sin omegat` and `x_(2) = A_(2)sin (omegat +(pi)/(4))`. The resultant `SHM` will have an amplitude of

A

`(A_(1)+A_(2))/(2)`

B

`sqrt(A_(1)^(2)+A_(2)^(2))`

C

`sqrt(A_(1)^(2)+A_(2)^(2)+sqrt(2)A_(1)A_(2))`

D

`A_(1)A_(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`A = sqrt(A_(1)^(2)+A_(2)^(2)+2A_(1)A_(2)cosphi)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • OSCILLATIONS

    NARAYNA|Exercise DISPLACEMENT|6 Videos

  • OSCILLATIONS

    NARAYNA|Exercise VELOCITY AND ACCELERATION|10 Videos

  • OSCILLATIONS

    NARAYNA|Exercise INTEGER ANSWER QUESTIONS|19 Videos

  • NEWTONS LAWS OF MOTION

    NARAYNA|Exercise PASSAGE TYPE QUESTION|6 Videos

  • PHYSICAL WORLD

    NARAYNA|Exercise C.U.Q|10 Videos

Similar Questions

Explore conceptually related problems

A particle is subjected to SHM as given by equation x_1=Asinomegat and x_2=A_2sin(omegat+(pi)/(3)) . The maximum acceleration and amplitude of the resultant motion are a_(max) and A , respectively Then.

A particle is subjected to two SHMs simultaneously X_(1) = a_(1) sinomegat and X_(2) = a_(2)sin(omegat + phi) Where a_(1) = 3.0 cm, a_(2) = 4.0 cm Find resultant amplitude if the phase difference phi has values (a) 0^(0) , (b) 60^(0) , (c) 90^(0)

Knowledge Check

  • x_(1)=A sin (omegat-0.1x) and x_(2)=A sin (omegat-0.1 x-(phi)/2) Resultant amplitude of combined wave is

    A
    `2A cos (phi)/4`
    B
    `Asqrt(2cosphi//2)`
    C
    `2A (phi)/2`
    D
    `Asqrt(2(1+cos(phi)/4))`

  • Two waves y_(1) =A_(1) sin (omega t - beta _(1)), y_(2)=A_(2) sin (omega t - beta_(2) Superimpose to form a resultant wave whose amplitude is

    A
    ` sqrt(A_(1)^(2)+ A_(2)^(2)+2A_(1)A_(2)cos (beta_(1)-beta_(2)))`
    B
    ` sqrt(A_(1)^(2)+ A_(2)^(2)+2A_(1)A_(2)sin (beta_(1)-beta_(2)))`
    C
    `A_(1) +A_(2)`
    D
    `|A_(1) +A_(2)|`

  • Equations y_(1) A sinomegat and y_(2) = A/2 sin omegat + A/2 cos omega t represent S.H.M. The ratio of the amplitudes of the two motions is

    A
    1
    B
    2
    C
    `0.5`
    D
    `sqrt2`

    • Similar Questions

    Explore conceptually related problems

    x_(1) = 5 sin (omegat + 30^(@)) x_(2) = 10 cos (omegat) Find amplitude of resultant SHM .

    (a) A particle is subjected to two simple harmonic motions x_1=A_1sin omegat and x_2=A_2 sin (omegat+pi//3) . Find (i) the displacement at t=0 , (ii) the maximum speed of the particle and (iii) the maximum acceleration of the particle. (b) A particle is subjected to two simple harmonic motions, one along the x-axis and the other on a line making an angle of 45^@ with the x-axis. The two motions are given by xy=x_0sinomegat and s=s_0sin omegat Find the amplitude of the resultant motion.

    x_(1) = 3 sin omega t ,x_(2) = 4 cos omega t Find (i) amplitude of resultant SHM, (ii) equation of the resultant SHM.

    x_(1) = 3 "sin" omega t , x_(2) = 4 "cos' omega t Find (i) amplitude of resultant SHM. (ii) equation of the resultant SHM.

    Two waves given by y_(1)=asinomegat and y_(2)=a sin (omegat+pi//2) reaching at a point superimpose. The resultant amplitude is

    Home
    Profile