Home
Class 12
PHYSICS
x(1) = 3 "sin" omega t , x(2) = 4 "cos' ...

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

Text Solution

Verified by Experts

First right all SHM's in terms of sine functions with positive amplitude. Keep "`omegat`" with positive sign `:. " " x_(1) = 3sin omega t`
` x_(2) = 4 sin (omegat + pi//2)`
`A=sqrt(3^(2)+4^(2)+2xx3xx4cos""(pi)/(2))`
=` sqrt(9+16) = sqrt(25) = 5 `
`tan phi = (4 sin ""(pi)/(2))/(3+4cos""(pi)/(2))=(4)/(3) " " phi = 53^(@)`
equation x = 5 sin`(omegat + 53^(@)`
Promotional Banner

Topper's Solved these Questions

  • SIMPLE HARONIC MOTION

    MOTION|Exercise EXERCISE -1 ( SECTION-A )|8 Videos

  • SIMPLE HARONIC MOTION

    MOTION|Exercise EXERCISE -1 ( SECTION-B ) (Time per iod and angu larfrequency in SHM)|8 Videos

  • SIMPLE HARMONIC MOTION

    MOTION|Exercise EXERCISE -3 Section - B Previous Year Problems | JEE MAIN|23 Videos

  • SOUND WAVES

    MOTION|Exercise Exercise - 3 (Section - B)|14 Videos

Similar Questions

Explore conceptually related problems

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

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

x_(1)= 5 sin (omega t + 30^(@)) , x2 = 10 cos ( omega t) Find amplitude of resultant SHM.

If i_(1)=3 sin omega t and (i_2) = 4 cos omega t, then (i_3) is

If i_(1) = 3 sin omega t and i_(2) =6 cos omega t , then i_(3) is

x_(1) = 3 sin omega t x_(2) = 5 sin (omega t + 53^(@)) x_(3) = - 10 cos omega t Find amplitude of resultant SHM.

The displacements of two intering lightwaves are y_(1) = 4 sin omega t and y_(2) = 3 cos(omega t) . The amplitude of the resultant wave is ( y_(1) and y_(2) are in CGS system)

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

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