Function $x$ = $A sin^2 wt + B cos^2 wt + C sin wt \  cos wt$ does not represents $SHM$ for this condition
  • AIf $A =0$; $B =0$ and $C \ne 0$
  • BIf $A = -B ; C = 2B,$ amplitude =$\left| {B\sqrt 2 } \right|$
  • CIf $A = B$ ; $C =0$
  • DIf $A =B$ ; $C = 2B,$ amplitude =$\left| B \right|$
Diffcult
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
    What is the period of small oscillations of the block of mass $m$ if the springs are ideal and pulleys are massless ?
    View Solution
  • 2
    A damped harmonic oscillator has a frequency of $5$ oscillations per second. The amplitude drops to half its value for every $10$ oscillations. The time it will take to drop to $\frac{1}{1000}$ of the original amplitude is close to .... $s$
    View Solution
  • 3
    A pendulum bob has a speed of $3\, {m} / {s}$ at its lowest position. The pendulum is $50 \,{cm}$ long. The speed of bob, when the length makes an angle of $60^{\circ}$ to the vertical will be $ .......\,{m} / {s}$ $\left(g=10 \,{m} / {s}^{2}\right)$
    View Solution
  • 4
    A simple harmonic oscillator has an amplitude $A$ and time period $6 \pi$ second. Assuming the oscillation starts from its mean position, the time required by it to travel from $x=A$ to $x=\frac{\sqrt{3}}{2} A$ will be $\frac{\pi}{x}$ s, where $x=$__________.
    View Solution
  • 5
    The amplitude of a particle executing $SHM$ about $O$ is $10\, cm.$ Then :
    View Solution
  • 6
    The time period of a simple pendulum is $2\, sec$. If its length is increased $4$ times, then its period becomes  ..... $\sec$
    View Solution
  • 7
    A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; $x = {a_1}\,\cos \,\omega t$ and $y = {a_2}\,\cos \,2\,\omega t$ traces a curve given by
    View Solution
  • 8
    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
  • 9
    A spring having a spring constant $‘K’$ is loaded with a mass $‘m’$. The spring is cut into two equal parts and one of these is loaded again with the same mass. The new spring constant is
    View Solution
  • 10
    A $3\ kg$ sphere dropped through air has a terminal speed of $25\ m/s$. (Assume that the drag force is $-bv$.) Now suppose the sphere is attached to a spring of force constant $k = 300\ N/m$, and that it oscillates with an initial amplitude of $20\ cm$. What is the angular frequencu of its damped $SHM$? ..... $rad/s$
    View Solution