When two displacements represented by $y_1 = asin\left( \omega t \right)$ and $y_2 = bcos\left(\omega t \right)$ are superimposed the motion is
  • A
    not a simple harmonic
  • Bsimple harmonic with amplitude $\frac{a}{b}$
  • Csimple harmonic with amplitude  $\sqrt {{a^2} + {b^2}} \;$
  • Dsimple harmonic with amplitude  $\frac{{\left( {a + b} \right)}}{2}$ 
AIPMT 2015, Medium
art

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Similar Questions

  • 1
    For a simple pendulum, a graph is plotted between its kinetic energy $(KE)$ and potential energy $(PE)$ against its displacement $d.$ Which one of the following represents these correctly ? (graphs are schematic and not drawn to scale)
    View Solution
  • 2
    A particle is executing Simple Harmonic Motion $(SHM)$. The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be
    View Solution
  • 3
    A simple pendulum hanging from the ceiling of a stationary lift has a time period $T_1$. When the lift moves downward with constant velocity, the time period is $T_2$, then
    View Solution
  • 4
    A body is executing $S.H.M.$ When its displacement from the mean position is $4\, cm$ and $5\, cm$, the corresponding velocity of the body is $10 \,cm/sec$ and $8\, cm/sec$. Then the time period of the body is
    View Solution
  • 5
    A particle executes simple harmonic motion and is located at $x = a, b$  and  $c$ at times $t_0, 2t_0$ and $3t_0$ respectively. The frequency of the oscillation is
    View Solution
  • 6
    Kinetic energy of a particle executing simple harmonic motion in straight line is $pv^2$ and potential energy is $qx^2$, where $v$ is speed at distance $x$ from the mean position. It time period is given by the expression
    View Solution
  • 7
    The velocity of simple pendulum is maximum at
    View Solution
  • 8
    $m x^{2}-b x+k=0$

    Find time after which to the energy will become half of initial maximum value in damped force oscillation.

    View Solution
  • 9
    A mass $m = 1.0\,kg$ is put on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is $500\,N/m.$ What is the amplitude $A$ of the motion, so that the mass $m$ tends to get detached from the pan ? (Take $g = 10\,m/s^2$ ). The spring is stiff enough so that it does not get distorted during the motion.
    View Solution
  • 10
    A $S.H.M.$ is represented by $x = 5\sqrt 2 (\sin 2\pi t + \cos 2\pi t).$ The amplitude of the $S.H.M.$ is .... $cm$
    View Solution