Waves Test - 63...

A particle performs simple harmonic motion with amplitude A. Its speed is trebled at the instant that it is at a distance $$\frac{2A}{3}$$ from equilibrium position. The new amplitude of the motion is  

The graph plotted between the velocity and displacement from mean position of a particle executing S,H.M. is

The amplitude of vibration of a particle is given by $${ a }_{ m }=\dfrac { { a }_{ 0 } }{ { a }w^{ 2 }-bw+c } $$ Where $${ a }_{ 0 },a,b$$ and $$ c$$ are positive. The condition for a single resultant frequency is

The amplitude of a wave represented by displacement equation $$ y=\frac{1}{\sqrt{a}}$$ $$\sin \omega t$$ $$\pm$$ $$\frac{1}{\sqrt{b}} $$ $$\cos \omega t$$ will be

A particle performs SHM of amplitude $$A$$ along a straight line. When it is at a distance $$\cfrac{\sqrt{3}}{2}A$$ from mean position, its kinetic energy gets increased by an amount $$\cfrac{1}{2}m \omega {A}^{2}$$ due to an impulsive force. Then its new amplitude becomes.

Displacement of a particle performing S.H.M. is given by  $$x = 0.01$$   $$\sin \pi ( t + 0.05 ) ,$$  where  $$x$$  is in meter and t is in seconds. The time period in second is : 

On the superposition of the two waves given as $${y}_{1}={A}_{0}\sin{(\omega t-kx)}$$ and $${y}_{2}={A}_{0}\cos {(\omega t-kx+\cfrac{\pi}{6}})$$ the resultant amplitude of oscillation will be

A particle performs S.H.M. of amplitude A along a straight line. When it is at a distance $$\frac{\sqrt 3}{2}$$ A form measure position, its kinetic energy gets increased by an amount $$\frac{1}{2}$$ m $$\omega^2A^2$$ due to an impulsive force. Then new amplitude becomes:

Two particles are executing SHM of same amplitude and frequency along the same straight line path. They pass each other when going in opposite directions, each time their displacement is half of their magnitude. What is the phase difference between them?

Four waves are expressed as
(i) $$y _ { 1 } = a _ { 1 } \sin \omega t$$                                            (ii) $$y _ { 2 } = a _ { 2 } \sin 2 \omega t$$
(iii) $$y _ { 3 } = a _ { 3 } \cos \omega t$$                                         (iv) $$y _ { 4 } = a _ { 4 } \sin ( \omega t + \phi )$$
The interference is possible between