Three simple harmonic motions of equal amplitudes $A$ and equal time periods in the same direction combine. The phase of the second motion is $60^o$ ahead of the first and the phase of the third motion is $60^o$ ahead of the second. Find the amplitude of the resultant motion
Medium
Download our app for free and get startedPlay store
Resultant of $1 \& 3$ is also $\mathrm{A}$ in the direction of $2.$

$\Delta \phi=120^{\circ}$ between $1 \& 3$

$A_{\text {net }}=A+A=2 A$

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
    The variation of kinetic energy $(KE)$ of a particle executing simple harmonic motion with the displacement $(x)$ starting from mean position to extreme position $(A)$ is given by
    View Solution
  • 2
    The displacement of a particle moving in $S.H.M.$ at any instant is given by $y = a\sin \omega t$. The acceleration after time $t = \frac{T}{4}$ is (where $T$ is the time period)
    View Solution
  • 3
    A particle has simple harmonic motion. The equation of its motion is $x = 5\sin \left( {4t - \frac{\pi }{6}} \right)$, where $x$ is its displacement. If the displacement of the particle is $3$ units, then it velocity is
    View Solution
  • 4
    The amplitude of a particle executing $SHM$ is $3\,cm$. The displacement at which its kinetic energy will be $25 \%$ more than the potential energy is: $.............cm$.
    View Solution
  • 5
    A particle of mass $m$ moves in the potential energy $U$ shown above. The period of the motion when the particle has total energy $E$ is
    View Solution
  • 6
    Two masses $m_1$ and $m_2$ are supended together by a massless spring of constant $k$. When the masses are in equilibrium, $m_1$ is removed without disturbing the system; the amplitude of vibration is
    View Solution
  • 7
    The potential energy of a simple harmonic oscillator at mean position is $2\,joules$. If its mean $K.E.$ is $4\,joules$, its total energy will be .... $J$
    View Solution
  • 8
    A particle is executing simple harmonic motion $(SHM)$ of amplitude $A,$ along the $x-$ axis, about $x = 0.$ When its potential energy $(PE)$ equals kinetic energy $(KE),$ the position of the particle will be
    View Solution
  • 9
    A simple pendulum is released from rest at the horizontally stretched position. When the string makes an angle $\theta$ with the vertical, the angle $\phi$ which the acceleration vector of the bob makes with the string is given by
    View Solution
  • 10
    particle moves with simple harmonic motion in a straight line. In first $\tau\ s$, after starting from rest it travels a distance $a$, and in next $\tau\ s$ it travels $2a$, in same direction, then
    View Solution