Two particles P and Q describe S.H.M. of same amplitude $a$, same frequency $f$ along the same straight line. The maximum distance between the two particles is a $\sqrt{2}$.The initial phase difference between the particle is -
Diffcult
Download our app for free and get started
(b)
$x _1= a \sin \left(\omega t +\phi_1\right), x _2= a \sin \left(\omega t +\phi_2\right)$
$\left| x _1- x _2\right|=2 a \sin \left(\omega t +\frac{\phi_1+\phi_2}{2}\right) \cos \left(\frac{\phi_1-\phi_2}{2}\right)$
To maximize $\left|x_1-x_2\right|: \sin \left(\omega t+\frac{\phi_1+\phi_2}{2}\right)=1$
$\Rightarrow a \sqrt{2}=2 a \times 1 \times \cos \left(\frac{\phi_1-\phi_2}{2}\right)$
$\Rightarrow \frac{1}{\sqrt{2}}=\cos \left(\frac{\phi_1-\phi_2}{2}\right) \Rightarrow \frac{\pi}{4}=\frac{\phi_1-\phi_2}{2}$
$\Rightarrow \phi_1-\phi_2=\frac{\pi}{2}$
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
- 1A pendulum has time period $T$. If it is taken on to another planet having acceleration due to gravity half and mass $ 9 $ times that of the earth then its time period on the other planet will beView Solution
- 2If a spring has time period $T$, and is cut into $n$ equal parts, then the time period of each part will beView Solution
- 3A body is executing simple harmonic motion with an angular frequency $2\,rad/s$. The velocity of the body at $20\, mm$ displacement, when the amplitude of motion is $60\, mm$, is ...... $mm/s$View Solution
- 4A body is executing $S.H.M.$ When its displacement from the mean position is $4\, cm$ and $5\, cm$, the corresponding velocity of the body is $10 \,cm/sec$ and $8\, cm/sec$. Then the time period of the body isView Solution
- 5The angular velocities of three bodies in simple harmonic motion are ${\omega _1},\,{\omega _2},\,{\omega _3}$ with their respective amplitudes as ${A_1},\,{A_2},\,{A_3}$. If all the three bodies have same mass and velocity, thenView Solution
- 6Two, spring $P$ and $Q$ of force constants $k_p$ and ${k_Q}\left( {{k_Q} = \frac{{{k_p}}}{2}} \right)$ are stretched by applying forces of equal magnitude. If the energy stored in $Q$ is $E$, then the energy stored in $P$ isView Solution
- 7The $x-t$ graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at $t=2 s$ is :View Solution
- 8A particle of mass m is executing oscillations about the origin on the $X-$axis. Its potential energy is $U(x) = k{[x]^3}$, where $k$ is a positive constant. If the amplitude of oscillation is $a$, then its time period $T$ isView Solution
- 9The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended, the period of oscillation will now beView Solution
- 10A pendulum suspended from the ceiling of a train has a period $T$ when the train is at rest. When the train travels same distance per unit time, the period of oscillation isView Solution