A particle starts from a point $P$ at a distance of $A/2$ from the mean position $O$ and travels towards left as shown in the figure. If the time period of $SHM$ , executed about $O$ is $T$ and amplitude $A$ then the equation of motion of particle is 
Medium
Download our app for free and get startedPlay store
$\mathrm{x}=\mathrm{A} \sin \left(\omega \mathrm{t}+\frac{\pi}{2}+\frac{\pi}{3}\right)$

$\mathrm{x}=\mathrm{A} \sin \left(\omega \mathrm{t}+\frac{5 \pi}{6}\right)=\mathrm{A} \sin \left(\frac{2 \mathrm{n}}{\mathrm{T}} \mathrm{t}+\frac{5 \mathrm{n}}{6}\right)$

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
    A particle moves in $xy$ plane according to the law $x = a \sin \omega t$ and $y = a(1-\cos \omega t)$ where $a$ and $\omega$ are constants. The particle traces
    View Solution
  • 2
    One-forth length of a spring of force constant $K$ is cut away. The force constant of the remaining spring will be
    View Solution
  • 3
    Displacement-time equation of a particle executing $SHM$ is $x\, = \,A\,\sin \,\left( {\omega t\, + \,\frac{\pi }{6}} \right)$ Time taken by the particle to go directly from $x\, = \, - \frac{A}{2}$ to $x\, = \, + \frac{A}{2}$ is
    View Solution
  • 4
    In a seconds pendulum, mass of bob is $30\, gm$. If it is replaced by $90\, gm$ mass. Then its time period will .... $\sec$
    View Solution
  • 5
    The frequency of oscillations of a mass $m$ connected horizontally by a spring of spring constant $k$ is $4 Hz$. When the spring is replaced by two identical spring as shown in figure. Then the effective frequency is,
    View Solution
  • 6
    A particle at the end of a spring executes simple harmonic motion with a period ${t_1}$, while the corresponding period for another spring is ${t_2}$. If the period of oscillation with the two springs in series is $T$, then
    View Solution
  • 7
    A spring is stretched by $0.20\, m$, when a mass of $0.50\, kg$ is suspended. When a mass of $0.25\, kg$ is suspended, then its period of oscillation will be .... $\sec$   $(g = 10\,m/{s^2})$
    View Solution
  • 8
    A $1\,kg$ mass is attached to a spring of force constant $600\,N / m$ and rests on a smooth horizontal surface with other end of the spring tied to wall as shown in figure. A second mass of $0.5\,kg$ slides along the surface towards the first at $3\,m / s$. If the masses make a perfectly inelastic collision, then find amplitude and time period of oscillation of combined mass.
    View Solution
  • 9
    A particle performs $S.H.M.$ of amplitude $A$ with angular frequency $\omega$  along a straight line. Whenit is at a distance  $\frac{{\sqrt 3 }}{2}$ $A$  from mean position, its kinetic energy gets increased by an amount $\frac{1}{2}m{\omega ^2}{A^2}$  due to an impulsive force. Then its new amplitude becomes
    View Solution
  • 10
    The diagram shows two oscillations. What is the phase difference between the oscillations?
    View Solution