Two simple harmonic motions are represented by equations ${y_1} = 4\,\sin \,\left( {10t + \phi } \right)$ and ${y_2} = 5\,\cos \,10\,t$ What is the phase difference between their velocities?
Medium
Download our app for free and get started
$y_{1}=4 \sin (10 t+\phi)$
$y_{2}=5 \cos 10 t$
$\Rightarrow \mathrm{y}_{2}=5 \sin \left(10 \mathrm{t}+\frac{\pi}{2}\right)$
phase difference $\frac{\pi}{2}-\phi$
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 rectangular block of mass $5\,kg$ attached to a horizontal spiral spring executes simple harmonic motion of amplitude $1\,m$ and time period $3.14\,s$. The maximum force exerted by spring on block is $.......N$.View Solution
- 2The motion of a simple pendulum excuting $S.H.M$. is represented by following equation.View Solution
$Y = A \sin (\pi t +\phi)$, where time is measured in $second$.
The length of pendulum is .............$cm$
- 3The velocity vector $v$ and displacement vector $x$ of a particle executing SHM are related as $\frac{v d v}{d x}=-\omega^2 x$ with the initial condition $v=v_0$ at $x=0$. The velocity $v$, when displacement is $x$, isView Solution
- 4A particle performs $SHM$ with a period $T$ and amplitude $a.$ The mean velocity of the particle over the time interval during which it travels a distance $a/2$ from the extreme position isView Solution
- 5A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $4 \mathrm{~m}$, then the time period of small oscillations will be ____ $s$. $\left[\right.$ take $\left.\mathrm{g}=\pi^2 \mathrm{~ms}^{-2}\right]$View Solution
- 6Aheavy brass sphere is hung from a light spring and is set in vertical small oscillation with a period $T.$ The sphere is now immersed in a non-viscous liquid with a density $1/10\,th$ the density of the sphere. If the system is now set in vertical $S.H.M.,$ its period will beView Solution
- 7A vertical mass spring system executes simple harmonic oscillations with a period of $2\,s$. A quantity of this system which exhibits simple harmonic variation with a period of $1\, sec$ isView Solution
- 8A particle of mass $m$ executes simple harmonic motion with amplitude $a$ and frequency $v$. The average kinetic energy during its motion from the position of equilibrium to the end isView Solution
- 9For a particle showing motion under the force $F=-5(x-2)^2$, the motion is .......View Solution
- 10A mass m oscillates with simple harmonic motion with frequency $f = \frac{\omega }{{2\pi }}$ and amplitude A on a spring with constant $K$ , thereforeView Solution