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As a result of adding two mutually perpe...

As a result of adding two mutually perpendicular oscillations of equal frequency the motion of an object occurs alongan ellipse, in one case the motion is clockwise, while in the other it is counter clockwise . Write the equations of motion along each coordinate axis, assuming that the initial phase along the x-axis is zero.

Text Solution

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x= A_(x) sin omegat , y = A_(y) sin (omegat + (pi)/(2))` for clockwise
`x= A_(x)sin omega t , y = A _(y) sin (omegat - ( pi)/(2)) ` for counter clockwise
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Knowledge Check

  • An object is moving with uniform acceleration a. Its initial velocity is u and after time t its velocity is v. The equation of its motion is v = u + at. The velocity (along y-axis) time (along x-axis) graph shall be a straight line

    A
    passing through origin
    B
    with x-intercept u
    C
    with y-intercept u
    D
    with slope u

  • The equation describing the motion of a simple harmonic oscillator along the X axis is given as x = A cos (omega t + phi) . If at time t = 0, the oscillator is at x = 0 and moving in the negative x direction, then the phase angle phi is

    A
    `(pi)/(2)`
    B
    `-(pi)/(2)`
    C
    `pi`
    D
    0

  • Two simple harmonic motions with the same frequency act on a particle at right angles i.e., along X-axis and Y-axis. If the two amplitudes are equal and the phase difference is pi//2 , the resultant motion will be

    A
    a circle
    B
    an ellipse with the major axis along Y-axis
    C
    an ellipse with the major axis along X-axis
    D
    a straight line inclined at `45^(@)` to the X-axis