Two particles are in $SHM$ on same straight line with amplitude $A$ and $2A$ and with same angular frequency $\omega .$ It is observed that when first particle is at a distance $A/\sqrt{2}$ from origin and going toward mean position, other particle is at extreme position on other side of mean position. Find phase difference between the two particles
Medium
Download our app for free and get started
Consider $2$ circles with radii $A \& 2 A$ and particles moving on them with constant angular velocity $\omega$
Choose $x$ axis to be horizontal on which the projection of the particles are to be taken.
When the projection of the first particle is at a distance $A / \sqrt{2}$ from origin, it is at an angle $45^{0}$ in the first quadrant.
whereas the second particle is at an angle $180^{0}$.
i.e the phase difference is $135^{0}$
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 are executing S.H.M. The equation of their motion are ${y_1} = 10\sin \left( {\omega \,t + \frac{{\pi T}}{4}} \right),$ ${y_2} = 25\sin \,\left( {\omega \,t + \frac{{\sqrt 3 \pi T}}{4}} \right)$. What is the ratio of their amplitudeView Solution
- 2On a planet a freely falling body takes $2 \,sec$ when it is dropped from a height of $8 \,m$, the time period of simple pendulum of length $1\, m$ on that planet is ..... $\sec$View Solution
- 3The length of a simple pendulum is increased by $2\%$. Its time period willView Solution
- 4Two bodies performing $SHM$ have same amplitude and frequency. Their phases at a certain instant are as shown in the figure. The phase difference between them isView Solution
- 5A particle of mass $m$ is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time $?$View Solution
- 6View SolutionIn damped oscillation graph between velocity and position will be
- 7The height of liquid column in a $U$ tube is $0.3$ meter. If the liquid in one of the limbs is depressed and then released, then the time period of liquid column will be $.......\,sec$View Solution
- 8The angular velocity and the amplitude of a simple pendulum is $\omega $ and $a$ respectively. At a displacement $X$ from the mean position if its kinetic energy is $T$ and potential energy is $V$, then the ratio of $T$ to $V$ isView Solution
- 9Which one of the following statements is true for the speed $v$ and the acceleration $a$ of a particle executing simple harmonic motionView Solution
- 10A particle free to move along the $x-$axis has potential energy given by $U(x) = k[1 - \exp {( - x)^2}]$ for $ - \infty \le x \le + \infty $, where k is a positive constant of appropriate dimensions. ThenView Solution