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Two particles are executing S.H.M of same amplitude and frequency along the same straight line path. They pass each other when going in opposite direction, each time their displacement is half of their amplitude. What is the phase difference between them?
(1) $5\mathrm{\pi }/6$
(2) $2\mathrm{\pi }/3$
(3) $\mathrm{\pi }/3$
(4) $\mathrm{\pi }/6$

A particle executes S.H.M. Then the graph of velocity as a function of displacement is:
(1) a straight line
(2) a circle
(3) an ellipse
(4) a hyperbola

A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes simple harmonic oscillations with a time period T. If the mass is increased by m, then the time period becomes $\left(\frac{5}{4}T\right)$. The ratio of $\frac{m}{M}$ is
(1) 9/16
(2) 5/4
(3) 25/16
(4) 4/5

Two masses $m_1 and m_2$ are suspended together by a massless spring of force constant k. When the masses are in equilibrium, $m_1$ is removed without disturbing the system. The amplitude of oscillation is:
(1) $\frac{m_{1}g}{k}$
(2) $\frac{m_{2}g}{k}$
(3) $\frac{(m_1+m_2)g}{k}$
(4) $\frac{(m_1-m_2)g}{k}$

Lissajous figure obtained by combining
x=a sin$\omega$t and y=a sin($\omega$t+$\pi$/4) will be:
(1) an ellipse
(2) straight line
(3) a circle
(4) a parabola

A particle of mass m is attached to three springs. A, B and C of equal force constant k. If the particle is pushed a little towards any one of the springs and left, find the time period of its oscillations.

(1) $2\mathrm{\pi }\sqrt{(\mathrm{m}/\mathrm{k})}$
(2) $2\mathrm{\pi }\sqrt{2m/k}$
(3) $2\mathrm{\pi }\sqrt{\mathrm{m}/\left(2\mathrm{k}\right)}$
(4) $2\mathrm{\pi }\sqrt{\mathrm{m}/3\mathrm{k}}$

A simple pendulum has a length l. The inertial and gravitational masses of the bob are $m_i and m_g$ respectively. Then the time period T is given by:
(1) $T=2\mathrm{\pi }\sqrt{\frac{{\mathrm{m}}_{\mathrm{g}}\mathrm{l}}{{\mathrm{m}}_{\mathrm{i}}\mathrm{g}}}$
(2) $T=2\mathrm{\pi }\sqrt{\frac{{\mathrm{m}}_{\mathrm{i}}\mathrm{l}}{{\mathrm{m}}_{\mathrm{g}}\mathrm{g}}}$
(3) $T=2\mathrm{\pi }\sqrt{\frac{{\mathrm{m}}_{\mathrm{i}}\times {\mathrm{m}}_{\mathrm{g}}\times \mathrm{l}}{\mathrm{g}}}$
(4) $T=2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{{\mathrm{m}}_{\mathrm{i}}\times {\mathrm{m}}_{\mathrm{g}}\times \mathrm{g}}}$

A and B are fixed points and the mass M is tied by strings at A and B. If the mass M is displaced slightly out of this plane and released, it will execute oscillations with period
(Given AM=BM=l, AB=2d)

(1) $2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{g}}}$
(2) $2\pi \sqrt{\frac{{\left(L^2-d^2\right)}^{1/2}}{g}}$
(3) $2\mathrm{\pi }\sqrt{\frac{{({\mathrm{L}}^2+{\mathrm{d}}^2)}^{1/2}}{\mathrm{g}}}$
(4) $2\mathrm{\pi }\sqrt{\frac{{\left(2\mathrm{d}\right)}^{3/2}}{\mathrm{g}}}$

A simple pendulum of length l is suspended from the roof of a cart that moves down on an inclined plane without friction. If $\theta$ is the inclination of the inclined plane to the horizontal, time period of oscillation of the pendulum is:
(1) $2\pi \sqrt{\frac{l \sin \theta }{g}}$
(2) $2\pi \sqrt{\frac{l \cos \theta }{g}}$
(3) $2\pi \sqrt{\frac{l }{g \cos \theta }}$
(4) $2\pi \sqrt{\frac{l }{g \sin \theta }}$

A pendulum suspended from the roof of an elevator at rest has a time period $T_1$; when the elevator moves up with an acceleration a, its time period becomes $T_2$; when the elevator moves down with accleration a, its time period becomes $T_3$; then
(1) $T_1=\sqrt{T_1^2+T_3^2}$
(2) $T_1=\sqrt{T_1{T}_2}$
(3) $T_1=\frac{T_2{T}_3\sqrt{2}}{\sqrt{T_2^2+T_3^2}}$
(4) $T_1=\frac{2T_2{T}_3}{\sqrt{T_2^2+T_3^2}}$

The transverse displacement y(x,t) of a wave on a string is given by
$y (x,t)=e^{-(a{x}^2+b{t}^2+2\sqrt{ab} xt)}$
This represents a 
(1)  wave moving in -x-direction with speed $\sqrt{\frac{b}{a}}$
(2) standing wave of frequency $\sqrt{b}$
(3) standing wave of frequency $\frac{1}{\sqrt{b}}$
(4) wave moving in +x direction with speed $\sqrt{\frac{a}{b}}$

An aluminium wire of length 60 cm is joined to a steel wire of length 80 cm and stretched between two fixed-supports. The tension produces is 40 N. Cross-sectional area is 1 $m{m}^2$ (Steel) and 3 $m{m}^2$ (aluminium). Minimum frequency of the tuning fork which can produce standing waves with the joint as node is (density of Al=2.6 g/cc and density of steel=7.8 g/cc)

(1) 90 Hz
(2) 145 Hz
(3) 180 Hz
(4) 250 Hz

The displacement due to a wave moving in the positive x-direction is given by y=$\frac{1}{(1+x^2)}$ at time t=0 and by y=$\frac{1}{[1+{(x-1)}^2]}$ at t=2s, where x and y are in meters. Velocity of the wave in m/s is
(1) 1 
(2) 0.5
(3) 2
(4) 4

Sound of wavelength $\lambda$ passes through a quinckes tube, which is adjusted to give a maximum intensity $I_0$. Through what distance should the sliding tube be moved to give an intensity $I_0$/2 ?
(1) $\frac{\lambda }{2}$
(2) $\frac{\lambda }{4}$
(3) $\frac{\lambda }{3}$
(4) $\frac{\lambda }{8}$

A uniform rope of mass 0.1 kg and length 2.45 m hangs from a ceiling. The time taken by the transverse wave to travel through the full length of the rope is
(1) 1.0 s
(2) 1.2 s
(3) 2.0 s
(4) 2.2 s

An open and closed organ pipe have the same length. The ratio of p^th mode of frequency of vibration of two pipes is
(1) 1
(2) p
(3) p(2p+1)
(4) $\frac{2p}{(2p-1)}$

A person P is 600 m away from a station when a train approaching station with 72 km/h, blows a whistle of frequency 800 Hz when 800 m away from the station. Find the frequency heard by the person. Speed of sound in air=300 ms^-1

(1) 800 Hz
(2) 845 Hz
(3) 829 Hz
(4) 843 Hz

The path difference between two waves
$y_1=a_1\sin \left(\omega t-\frac{2\mathrm{\pi x}}{\lambda }\right) and$
$y_2=a_2\cos \left(\omega t-\frac{2\mathrm{\pi x}}{\lambda }+\varphi \right) is$
(1) $\frac{\lambda }{2\pi }\left(\varphi \right)$
(2) $\frac{\lambda }{2\pi }\left(\varphi +\frac{\mathrm{\pi }}{2}\right)$
(3) $\frac{2\mathrm{\pi }}{\lambda }\left(\varphi -\frac{\mathrm{\pi }}{2}\right)$
(4) $\frac{2\mathrm{\pi }}{\lambda }\left(\varphi \right)$
 

If the temperature is raised by 1 K from 300 K the percentage change in the speed of sound in the gaseous mixture is (R=8.31 J/mole-K)
(1) 0.167 %
(2) 0.334%
(3) 1%
(4) 2%

In a sonometer wire, the tension is maintained by suspending a 50.7 kg mass from the free end of the wire. The suspended mass has a volume of 0.0075 m³. The fundamental frequency of the wire is 260 Hz. If the suspended mass is completely submerged in water, the fundamental frequency will become
(1) 200 Hz
(2) 220 Hz
(3) 230 Hz
(4) 240 Hz