CBSE Questions for Class 11 Engineering Physics Oscillations Quiz 8 - MCQExams.com

Springs of spring constants K, 2K, 4K, 8K, 2048 K are connected in series. A mass 'm' is attached to one end the system is allowed to oscillation. The time period is approximately :
  • $$2\pi \sqrt{\dfrac{m}{2K}}$$
  • $$2\pi \sqrt{\dfrac{2m}{2K}}$$
  • $$2\pi \sqrt{\dfrac{2m}{K}}$$
  • none of these
A block of mass m is suspended separately by two different springs have time period $${ t }_{ 1 }$$ and $${ t }_{ 2 }$$. If same mass is connected to parallel combination of both springs, then its time period is $$T$$. Then
  • $$T = t_1 + t_2$$
  • $$T^2 = t_1^2 + t_2^2$$
  • $$T^{-1} = t_1^{-1} + t_2^{-1}$$
  • $$T^{-2} = t_1^{-2} + t_2^{-2}$$
The bob of a $$0.2 m$$ pendulum describes an arc of circle in a vertical plane. If the tension in the cord is $$\sqrt { 3 }$$ times the weight of the bob when the cord makes an angle $$30$$ with the vertical, the acceleration of the bob in that position is
  • $$9.8$$
  • $$6.02$$
  • $$7.2$$
  • $$5.2$$
A point mass oscillates along the $$x$$ -axis according to the law $$x = x _ { 0 } \cos ( \omega t - \pi / 4 )$$. If the acceleration of the particle is written as $$a = A \cos ( \omega t + \delta )$$ then:
  • $$A = x _ { 0 } , \delta = - \pi / 4$$
  • $$A = x _ { 0 } \omega ^ { 2 } , \delta = - \pi / 4$$
  • $$A = x _ { 0 } \omega ^ { 2 } , \delta = - \pi / 8$$
  • $$A = x _ { 0 } \omega ^ { 2 } , \delta = 3 \pi / 4$$
A simple pendulum has time period $$T _ { 1 }.$$ The point of suspension is now moved upward according to equation $$y = K t ^ { 2 }$$ where $$K = 2.5 \mathrm { m } / \mathrm { s } ^ { 2 }.$$ If new time period is $$T _ { 2 }$$ then ratio will be
  • $$2 / 3$$
  • $$5 / 6$$
  • $$6 / 5$$
  • $$3 / 2$$
A particle undergoes SHM. When its displacement is 8 cm, it has speed 3 m/s and a speed 4 m/s at displacement of 6cm. Find time period of oscillation.
  • $$4\pi$$
  • $$6\pi$$
  • $$7\pi$$
  • $$8\pi$$
The time period of oscillation of a $$SHM$$ is $$\frac { \pi } { 2 } s.$$ Its acceleration at a phase angle $$\frac { \pi } { 3 }\ rad$$  from extreme position is $$2 m s ^ { - 2 }.$$ What is its velocity at a displacement equal to half of its amplitude from mean position? (in $$m s ^ { - 1 }$$)
  • $$0.707$$
  • $$0.866$$
  • $$\sqrt { 2 }$$
  • $$\sqrt { 3 }$$
If function $$\sin^{2}(\omega t)$$ represents position of a particle from the origin as function of time, then motion of particle is
  • A simple harmonic motion with a period $$2\pi/\omega$$
  • A simple harmonic motion with a period $$\pi/\omega$$
  • A period motion but not simple harmonic motion with a period $$2\pi/\omega$$
  • A period motion but not simple harmonic motion with a period $$\pi/\omega$$
If the maximum velocity of a particle in SHM is $${ v }_{ 0 }$$. then its velocity at half the amplitude from position  of rest will be :
  • $${ v }_{ 0 }/2$$
  • $${ v }_{ 0 }$$
  • $${ v }_{ 0 }\sqrt { \dfrac{3}{2} } $$
  • $$\dfrac{{ v }_{ 0 }\sqrt { 3 }}{2}$$
A block of mass $$10\,Kg$$ is suspended through two light spring balances as shown in figure.


1205988_cc29096b208b45adbb8fa252879d799e.png
  • Both the scales will read $$10\,Kg$$
  • Both the scales will read $$5\,Kg$$
  • The upper scale will read $$10\,Kg$$ and the lower zero
  • The readings may be anything but their sum will be $$10\,Kg$$
A particle is executing S.H.M. with amplitude $$'a'$$ and has maximum velocity $$'v'$$. Its speed at displacement $$a/2$$ will be
  • $$0.866\ v$$
  • $$v/2$$
  • $$v$$
  • $$v/4$$
A particle moves along a straight line such that its displacement(s) at any time(t) is given by $$S=t^3-3t^2+2$$. The velocity of the particle when its acceleration zero is?
  • $$-2$$ units
  • $$-8$$ units
  • $$0$$ units
  • $$-9$$ units
The time period of a particle in simple  harmonic motion is equal to the time between consecutive apperance of the particle at a particular point in its motion. This point is 
  • The mean position
  • An extreme position
  • Between the mean position and the positive extreme
  • Between the mean position and the negative extreme
A particle executing $$SHM$$ while moving from the one extremity is found at distance $$x_1, x_2$$ and $$x_3$$ from the centre at the end of three successive seconds. The time period of oscillation is   
  • $$\dfrac{2\pi}{\theta}$$
  • $$\dfrac{\pi}{\theta}$$
  • $$\theta$$
  • $$\dfrac{\pi}{2\theta}$$
The plot of velocity (v) versus displacement (x) of a particle executing simple harmonic motion is shown in figure. The time period of oscillation of particle is
1191262_a59d628b7c024ea7a5426f5ecaa4a7f3.PNG
  • $$\dfrac { \pi }{ 2 } s$$
  • $$\pi s$$
  • $$2\pi s$$
  • $$3\pi s$$
A simple pendulum has the time period of T at the surface of Earth. if it is taken to a height equal to R above the surface of Earth, then the new time period will be :
  • T
  • 4T
  • $$\sqrt{2}T$$
  • 2T
A cubical body of side $${10}^{-1}m$$ and mass $$2\times {10}^{-3}kg$$ is floating in water. When it is  pressed inside water and then released. It executes SHM its time period will be 
  • $$28\ sec$$
  • $$0.028\ sec$$
  • $$0.28\ sec$$
  • $$2.8\ sec$$
A stone falls freely from rest a height $$h$$ and it travels a distance of$$\dfrac{h}{2}$$ in the last second.The time of journey is
  • $$\sqrt 2s$$
  • $$(2- \sqrt 2)s$$
  • $$(2+\sqrt 2)s$$
  • $$2s$$
The differential equation representing the SHM of a particuleis $$\cfrac{9d^2y} {dt^2}+4y=0$$. The time period of the particle is given by
  • $$\cfrac\pi 3 {sec}$$
  • $$\pi {sec}$$
  • $$\cfrac2\pi 3 {sec}$$
  • $$3\pi {sec}$$
The force of a required to row a boat at velocity is proportional to square of its speed of v km/ h requires 4 KW, how many does a seepd of 2V km/h required 
  • 8 kW
  • 16 kW
  • 32kw
  • 76kw
The differential equation representing the SHM of a particule is $$\dfrac { { 9d }^{ 2 }y }{ { dt }^{ 2 } } $$ $$+ 4y = 0.$$ The time period of the particle is given by :
  • $$\dfrac\pi 3\ sec$$
  • $$\pi\ sec$$
  • $$\dfrac { 2\pi }{ 3 }\ sec$$
  • $$3\pi\ sec$$
Spring in vehicles are introduces to:
  • Reduce
  • Reduce impluse
  • Reduce force
  • Reduce velocity
A particle executing $$S.H.M$$ of amplitude $$4\ cm$$ and $$T=4\ sec$$. The time taken by it move from positive extreme position to half the amplitude is:-
  • $$1\ sec$$
  • $$\dfrac {1}{3}\ sec$$
  • $$\dfrac {2}{3}\ sec$$
  • $$\sqrt{\dfrac {2}{3}}\ sec$$
A particle oscillating in simple harmonic motion is :
  • Never in equilibrium because it is in motion
  • Never in equilibrium because there is always a force
  • In equilibrium at the ends of its path because of zero velocity there
  • In equilibrium at the centre of its path because the acceleration is zero there
A particle is executing $$S.H.M.$$ If the amplitude is $$2m$$ and periodic time $$2 \ \ seconds$$, then the max. velocity of the particle will be
  • $$\pi m/s$$
  • $$\sqrt 2 \pi m/s$$
  • $$2 \pi m/s$$
  • $$4 \pi m/s$$
A spring-block system undergoes simple harmonic motion on a smooth horizontal surface. The block is now given some positive charge, and a uniform horizontal electric field to the right is switched on. As a result,

1219052_18aaa54590de4282bac428418d9de7c7.jpg
  • the time period of oscillation will increase
  • the time period of oscillation will decrease
  • the time period of oscillation will remain unaffected
  • the mean position of simple harmonic motion will shift to the left
A particle performs SHM with period T and amplitude A. The mean velocity of the particle averaged over quarter oscillation, starting from right extreme position is
  • $$0$$
  • $$\dfrac{2A}{T}$$
  • $$\dfrac{4A}{T}$$
  • $$\dfrac{3A}{T}$$
A body of mass $$100 gm$$ is performing $$S.H.M$$ with a period of $$4.5s$$ and amplitude $$7 cm$$ . Velocity of the body at equilibrium position in $$cm/s$$ is
  • $$10$$
  • $$8$$
  • $$6$$
  • $$5$$
A particle executes SHM of type $$x=asin\omega t$$. It takes time $$t_1$$ from $$x=0$$ to $$x=\dfrac{a}{2}$$  and $$t_2$$ from $$x=\dfrac{a}{2}$$ $$t_2$$ from $$x=\dfrac{a}{2}$$ to $$x=a$$. The ratio of $$t_1:t_2$$ will be:
  • $$1:1$$
  • $$1:2$$
  • $$1:3$$
  • $$2:1$$
An object exceuting SHM has an acceleration of $$0.2m/s^{2}$$ at a distance of $$0.05$$m from the mean position calculate the period of SHM
  • $$2.1435$$
  • $$3.1428$$
  • $$1.432$$
  • $$4.321$$
The acceleration of a particle in $$SHM$$ at $$5\ cm$$ from its mean position is 20 $$cm/{ sec }^{ 2 }$$. The value of angular frequency in radians/ sec will be :
  • $$2$$
  • $$4$$
  • $$10$$
  • $$14$$
The amplitude and time period of a particle performing $$S.H.M$$ are ;a;and $$T$$ respectively. The displacement at which its velocity will be  half the max. velocity will be
  • $$\dfrac{a}{2}$$
  • $$\dfrac{a}{3}$$
  • $$\sqrt 3 {\dfrac{a}{2}}$$
  • $$\dfrac{2a}{\sqrt 3}$$
The position vector of a particle from origin is given by $$\hat r = A\left( {\hat i\cos \omega t + \hat jsin\omega t} \right)$$. The motion of the particle is
  • simple harmonic
  • on a straight line
  • on a circle
  • with contact acceleration
A particle is subjected to two simple harmonic motions given by:
$$y_1=10 \sin\omega t$$ and $$y_2=5 \sin (\omega t+ \pi)$$ The maximum speed of the particle is:
  • $$\sqrt{10^2+5^2 \omega}$$
  • $$\sqrt{10^2-5^2 \omega}$$
  • $$5\omega$$
  • $$15\omega$$
The maximum time period of oscillation of a simple pendulum of larger length is :
  • $$Infinity$$
  • $$24\ hours$$
  • $$12\ hours$$
  • $$1\ 1/2\ hours$$
$$\upsilon $$ as shown in figure. The velocity of the block on the plane 'u' is
1228836_cacfacd054044e92b762d757c7062b14.png
  • $$\upsilon$$ cos $$ec \theta$$
  • $$\upsilon$$ sin $$ \theta$$
  • $$\upsilon$$ cos $$ \theta$$
  • $$\upsilon$$ sec $$ \theta$$
A particle of mass $$2$$kg, executing SHM has amplitude $$20$$cm and time period $$1$$s. Its maximum speed is
  • $$0.314$$m/s
  • $$0.628$$m/s
  • $$1.256$$m/s
  • $$2.512$$m/s
A particle executes SHM of time period T. It takes time $$t_1$$ to go from $$x=0$$  to $$x = \frac{a}{2}$$  and $${t_2}$$ from $$x = \frac{a}{2}$$ to $$x=0$$. The ratio of $${t_1}:{t_2}$$ will be:
  • 1:1
  • 1:2
  • 1:3
  • 2:1
Two particles executes S.H.M along the same line at the same frequency. They move in opposite direction at the mean position. The phase difference will be :
  • $$2\pi $$
  • $$2\pi /3$$
  • $$\pi $$
  • $$\pi /2$$
A particle has simple harmonic motion. The equa-tion of its motion is $$x=5\sin (4t- \pi / 6)$$, where $$x$$ is its displacement. If the displacement of the particle is $$3\ units$$, then its velocity is
  • $$2 \pi /3$$ units
  • $$5 \pi /6$$ units
  • $$20$$ units
  • $$16$$ units
The maximum speed of a particle executing $$SHM$$ is $$1\ m/s$$ and maximum acceleration is $$1.57m/s^{2}$$. Its time period is
  • $$1s$$
  • $$4s$$
  • $$2s$$
  • $$3s$$
If a hallow spherical vessel is slowly filed up to middle with water, then its period of oscillation
  • first increases then decreases
  • Remains same
  • increases
  • decreases
A particle starts simple harmonic motion from the mean position. Its amplitude is a and total energy E. At one instant its kinetic energy is 3E/Its displacement at the instat is-
  • $$a/\sqrt { 2 } $$
  • $$a/2$$
  • $$\dfrac { a }{ \sqrt { 3/2 } } $$
  • $$a/\sqrt { 3 } $$
A particle is executing $$SHM$$ along $$x$$-axis given by $$x = A  \sin \omega t$$. The average velocity during the time interval $$t = 0$$ to $$t = T$$ is 
  • $${4A}/{T}$$
  • $$0$$
  • $${2A}/{T}$$
  • $${A}/{T}$$
A wave has SHM whose period is 4 s while another wave which also possess SHM has its period 3 s. If both are combined, then the resultant wave will have the period equal to:
  • 4 s
  • 5 s
  • 12 s
  • 3 s
Time period of a particle executing $$SHM$$ is $$8\ sec$$. At $$t=0$$ it is at the mean position. The ratio of the distance covered by the particle in the $$1st$$ second to the $$2nd$$ second is :
  • $$\dfrac{1}{\sqrt{2}+1}$$
  • $$\sqrt{2}$$
  • $$\dfrac{1}{\sqrt{2}}$$
  • $$\sqrt{2}+1$$
A string of mass m is fixed at both ends. The fundamental tone oscillations are excited in the strong with angular frequency $$\omega $$ and maximum displacement amplitude A. Find the total energy curtained in the string.
  • $$\frac { 1 }{ 2 } { m\omega }^{ 2 }{ A }^{ 2 }$$
  • $$\frac { 1 }{ 4 } { m\omega }^{ 2 }{ A }^{ 2 }$$
  • $$\frac { 1 }{ 6 } { m\omega }^{ 2 }{ A }^{ 2 }$$
  • $$\frac { 1 }{ 8 } { m\omega }^{ 2 }{ A }^{ 2 }$$
A dog of mass $$m$$ is walking on a pivoted disc of radius $$R$$ and mass $$M$$ in a circle of radius $$R/2$$ with an angular frequency $$n$$. The disc will revolve in opposite direction with frequency :
1248132_a37724658a824ce79691e57064385bef.png
  • $$\dfrac{mn}{M}$$
  • $$\dfrac{mn}{2M}$$
  • $$\dfrac{2 mn}{M}$$
  • $$\dfrac{2Mn}{M}$$
A particle executes simple harmonic motion between x = - A  and x = + A .The time taken by it to go from O to A /2 is T$$_{1}$$ and to go from  A /2 to  A is T$$_{2}$$. Then 
  • T$$_{1}$$< T$$_{2}$$
  • T$$_{1}$$ > T$$_{2}$$
  • T$$_{1}$$ = T$$_{2}$$
  • T$$_{1}$$ = 2 T$$_{2}$$
A uniform straight rod of mass 'm; kg and length L is hinged at one end. It is free to oscillate in vertical plane. A point of mass (m kg) is attached to it at a distance 'x' from the hinge. The value of x for which time period of oscillations will be minimum is (use: $$\sqrt { \frac { 7 }{ 3 } =1.5 } $$)
  • $$2L/3$$
  • $$L/2$$
  • $$L/4$$
  • $$2L/7$$
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