$Y = A \sin \left(\omega t +\phi_{0}\right)$ is the time-displacement equation of a SHM. At $t=0$ the displacement of the particle is $Y =\frac{ A }{2}$ and it is moving along negative $x$ -direction. Then the initial phase angle $\phi_{0}$ will be ...... .
JEE MAIN 2021, Diffcult
Download our app for free and get started
initial phase $\frac{\pi}{2}+\frac{\pi}{3}=\frac{5 \pi}{6}$
Download our appand 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
- 1Two particles $P$ and $Q$ describe simple harmonic motions of same period, same amplitude, along the same line about the same equilibrium position $O.$ When $P$ and $Q$ are on opposite sides of $O$ at the same distance from $O$ they have the same speed of $1.2 \,m/s$ in the same direction, when their displacements are the same they have the same speed of $1.6\, m/s$ in opposite directions. The maximum velocity in $m/s$ of either particle isView Solution
- 2The displacements of two particles executing $S.H.M.$ on the same line are given. as $y_1=a \sin \left(\frac{\pi}{2} t+\phi\right)$ and $y_2=b \sin \left(\frac{2 \pi}{3} t+\phi\right)$. The phase difference between them at $t=1 \,s$ is .........View Solution
- 3A mass $M$ is suspended from a light spring. An additional mass m added displaces the spring further by a distance $x$. Now the combined mass will oscillate on the spring with periodView Solution
- 4There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is $T$. If the resultant acceleration becomes $g/4,$ then the new time period of the pendulum isView Solution
- 5A particle is subjected to two mutually perpendicular simple harmonic motions such that its $x$ and $y$ coordinates are given by ?View Solution
$ x = 2 \sin \omega t \,;$ $ y = 2 \sin \left( {\omega t + \frac{\pi }{4}} \right)$
The path of the particle will be :
- 6A pendulume clock loses $12\;s$ a day if the temperature is $40^oC$ and gains $4\;s$ a day if the temperature is $20^oC$. The temperature at which the clock will show correct time, and the coeffecient of linear expansion $(\alpha)$ of the metal of the pendulum shaft are respectivelyView Solution
- 7If a spring of stiffness $k$ is cut into two parts $A$ and $B$ of length $l_{A}: l_{B}=2: 3$, then the stiffness of spring $A$ is given byView Solution
- 8View SolutionTwo mutually perpendicular simple harmonic vibrations have same amplitude, frequency and phase. When they superimpose, the resultant form of vibration will be
- 9Out of the following functions representing motion of a particle which represents $SHM$View Solution
$(A)\;y= sin\omega t-cos\omega t$
$(B)\;y=sin^3\omega t$
$(C)\;y=5cos\left( {\frac{{3\pi }}{4} - 3\omega t} \right)$
$(D)\;y=1+\omega t+{\omega ^2}{t^2}$
- 10A mass $m = 8\,kg$ is attahced to a spring as shown in figure and held in position so that the spring remains unstretched. The spring constant is $200\,N/m$. The mass $m$ is then released and begins to undergo small oscillations. The maximum velocity of the mass will be ..... $m/s$ $(g = 10\,m/s^2)$View Solution
