STD 11 - Oscillations PYQs: JEE Mains Physics – Page 2

Showing 51–100 of 158 questions

51. 51. At a given point of time the value of displacement of a simple harmonic oscillator is given as \(y = A \cos \left(30^{\circ}\right)\). If amplitude is \(40\,cm\) and kinetic energy at that time is \(200\, J\), the value of force constant is \(1.0 \times 10^{ x }\,Nm ^{-1}\). The value of \(x\) is ...... 2023 Hard
52. 52. For a periodic motion represented by the equation \(Y=\sin \omega t+\cos \omega t\) The amplitude of the motion is  2023 Easy
53. 53. For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is \(1\,kg\), the angular frequency is \(\omega_1\). When the mass block is \(2\,kg\) the angular frequency is \(\omega_2\). The ratio \(\omega_2 / \omega_1\) is
    2023 Easy
54. 54. In a linear simple harmonic motion \((SHM)\) \((A)\) Restoring force is directly proportional to the displacement. \((B)\) The acceleration and displacement are opposite in direction. \((C)\) The velocity is maximum at mean position. \((D)\) The acceleration is minimum at extreme points. Choose the correct answer from the options given below : 2023 Medium
55. 55. In the figure given below. a block of mass \(M =490\,g\) placed on a frictionless table is connected with two springs having same spring constant \(\left( K =2 N m ^{-1}\right)\). If the block is horizontally displaced through ' \(X\) 'm then the number of complete oscillations it will make in \(14 \pi\) seconds will be \(.........\)
    2023 Medium
56. 56. The amplitude of a particle executing \(SHM\) is \(3\,cm\). The displacement at which its kinetic energy will be \(25 \%\) more than the potential energy is: \(.............cm\). 2023 Medium
57. 57. The general displacement of a simple harmonic oscillator is \(x = A \sin \omega t\). Let \(T\) be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when \(t=\frac{T}{\beta}\). The value of \(\beta\) is \(.........\) 2023 Hard
58. 58. The maximum potential energy of a block executing simple harmonic motion is \(25\,J\). A is amplitude of oscillation. At \(A / 2\), the kinetic energy of the block is \(...............\) 2023 Easy
59. 59. The velocity of a particle executing SHM varies with displacement \(( x )\) as \(4 v ^2=50- x ^2\). The time period of oscillations is \(\frac{x}{7} s\). The value of \(x\) is \(............\) \(\left(\right.\) Take \(\left.\pi=\frac{22}{7}\right)\) 2023 Medium
60. 60. Two simple harmonic waves having equal amplitudes of \(8\,cm\) and equal frequency of \(10\,Hz\) are moving along the same direction. The resultant amplitude is also \(8\,cm\). The phase difference between the individual waves is \(..................\) degree. 2023 Medium
61. 61. A body is performing simple harmonic with an amplitude of \(10 \,cm\). The velocity of the body was tripled by air Jet when it is at \(5 \,cm\) from its mean position. The new amplitude of vibration is \(\sqrt{ x } \,cm\). The value of \(x\) is________ 2022 Hard
62. 62. A mass \(0.9\,kg\), attached to a horizontal spring, executes \(SHM\) with an amplitude \(A _{1}\). When this mass passes through its mean position, then a smaller mass of \(124\,g\) is placed over it and both masses move together with amplitude \(A _{2}\). If the ratio \(\frac{ A _{1}}{ A _{2}}\) is \(\frac{\alpha}{\alpha-1}\), then the value of \(\alpha\) will be\(......\) 2022 Hard
63. 63. A particle executes simple harmonic motion. Its amplitude is \(8 \,cm\) and time period is \(6 \,s\). The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is ............. \(s\) 2022 Medium
64. 64. A pendulum is suspended by a string of length \(250\,cm\). The mass of the bob of the pendulum is \(200\,g\). The bob is pulled aside until the string is at \(60^{\circ}\) with vertical as shown in the figure. After releasing the bob. the maximum velocity attained by the bob will be________ \(ms ^{-1}\). (if \(g=10\,m / s ^{2}\) )
    2022 Medium
65. 65. As per given figures, two springs of spring constants \(K\) and \(2\,K\) are connected to mass \(m\). If the period of oscillation in figure \((a)\) is \(3 s\), then the period of oscillation in figure \((b)\) will be \(\sqrt{ x }\) s. The value of \(x\) is\(.........\)
    2022 Medium
66. 66. In figure \((A),\) mass ' \(2 m\) ' is fixed on mass ' \(m\) ' which is attached to two springs of spring constant \(k\). In figure \((B),\) mass ' \(m\) ' is attached to two spring of spring constant ' \(k\) ' and ' \(2 k\) '. If mass ' \(m\) ' in \((A)\) and \((B)\) are displaced by distance ' \(x\) ' horizontally and then released, then time period \(T_{1}\) and \(T_{2}\) corresponding to \((A)\) and \((B)\) respectively follow the relation.
    2022 Medium
67. 67. The displacement of simple harmonic oscillator after \(3\) seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is \(\dots \; s\) 2022 Medium
68. 68. The equation of a particle executing simple harmonic motion is given by \(x =\sin \pi\left( t +\frac{1}{3}\right) m\). At \(t =1 \,s\), the speed of particle will be .......... \(cm s ^{-1}\) (Given : \(\pi=3.14\) ) 2022 Medium
69. 69. The metallic bob of simple pendulum has the relative density \(5\). The time period of this pendulum is \(10\,s\). If the metallic bob is immersed in water, then the new time period becomes \(5 \sqrt{ x } s\). The value of \(x\) will be. 2022 Medium
70. 70. The motion of a simple pendulum excuting \(S.H.M\). is represented by following equation. \(Y = A \sin (\pi t +\phi)\), where time is measured in \(second\). The length of pendulum is .............\(cm\) 2022 Medium
71. 71. The potential energy of a particle of mass \(4\,kg\) in motion along the \(x\)-axis is given by \(U =4(1-\cos 4 x )\,J\). The time period of the particle for small oscillation \((\sin \theta \simeq \theta)\) is \(\left(\frac{\pi}{ K }\right)\,s\). The value of \(K\) is ....... 2022 Hard
72. 72. Time period of a simple pendulum in a stationary lift is ' \(T\) '. If the lift accelerates with \(\frac{ g }{6}\) vertically upwards then the time period will be ..... (where \(g =\) acceleration due to gravity) 2022 Medium
73. 73. Two massless springs with spring constants \(2\,k\) and \(9\,k\), carry \(50\, g\) and \(100 \,g\) masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be 2022 Easy
74. 74. Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the \(\sqrt{3}\) times of amplitude of individual motions. The phase difference between the two motions is \(.....(degree)\) 2022 Medium
75. 75. When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be. 2022 Medium
76. 76. A block of mass \(1 \,kg\) attached to a spring is made to oscillate with an initial amplitude of \(12\, cm\). After \(2\, minutes\) the amplitude decreases to \(6\, cm\). Determine the value of the damping constant for this motion. (take In \(2=0.693\) ) 2021 Hard
77. 77. A bob of mass \('m'\) suspended by a thread of length \(l\) undergoes simple harmonic oscillations with time period \({T}\). If the bob is immersed in a liquid that has density \(\frac{1}{4}\) times that of the bob and the length of the thread is increased by \(1 / 3^{\text {rd }}\) of the original length, then the time period of the simple harmonic oscillations will be :- 2021 Hard
78. 78. A mass of \(5\, {kg}\) is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length \(4\, {m}\) has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed? (In \({m} / {s}^{2}\))
    2021 Hard
79. 79. A particle executes \(S.H.M.,\) the graph of velocity as a function of displacement is :- 2021 Medium
80. 80. A particle executes \(S.H.M.\) with amplitude \('a'\) and time period \(V\). The displacement of the particle when its speed is half of maximum speed is \(\frac{\sqrt{ x } a }{2} .\) The value of \(x\) is \(\ldots \ldots \ldots\) 2021 Medium
81. 81. A particle executes simple harmonic motion represented by displacement function as \(x(t)=A \sin (\omega t+\phi)\) If the position and velocity of the particle at \(t=0\, {s}\) are \(2\, {cm}\) and \(2\, \omega \,{cm} \,{s}^{-1}\) respectively, then its amplitude is \(x \sqrt{2} \,{cm}\) where the value of \(x\) is ..... . 2021 Medium
82. 82. A particle of mass \(1\, {kg}\) is hanging from a spring of force constant \(100\, {Nm}^{-1 .}\) The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period \({T}\). The time when the kinetic energy and potential energy of the system will become equal, is \(\frac{{T}}{{x}}\). The value of \({x}\) is ..... . 2021 Hard
83. 83. A particle performs simple harmonic motion with a period of \(2\) second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is \(\frac{1}{ a } s .\) The value of \('a'\) to the nearest integer is......... 2021 Medium
84. 84. 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 \(3E/4.\) Its displacement at that instant is 2021 Medium
85. 85. A pendulum bob has a speed of \(3\, {m} / {s}\) at its lowest position. The pendulum is \(50 \,{cm}\) long. The speed of bob, when the length makes an angle of \(60^{\circ}\) to the vertical will be \( .......\,{m} / {s}\) \(\left(g=10 \,{m} / {s}^{2}\right)\) 2021 Medium
86. 86. Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass \(=500\, g\), Decay constant \(=20 \,g / s\) then ...... \(s\) time is required for the amplitude of the system to drop to half of its initial value ? \((\ln 2=0.693)\) 2021 Hard
87. 87. An object of mass \(0.5\, {kg}\) is executing simple harmonic motion. Its amplitude is \(5\, {cm}\) and time period (T) is \(0.2\, {s} .\) What will be the potential energy of the object at an instant \(t=\frac{T}{4}\) s starting from mean position. Assume that the initial phase of the oscillation is zero. (In \({J}\)) 2021 Medium
88. 88. Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance \(( R / 2)\) from the earth's centre, where \('R'\) is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period 2021 Hard
89. 89. Consider two identical springs each of spring constant \(k\) and negligible mass compared to the mass \(M\) as shown. Fig. \(1\) shows one of them and Fig. \(2\) shows their series combination. The ratios of time period of oscillation of the two \(SHM\) is \(\frac{ T _{ b }}{ T _{ a }}=\sqrt{ x },\) where value of \(x\) is (Round off to the Nearest Integer)
    2021 Medium
90. 90. For a body executing \(S.H.M. :\) \((a)\) Potential energy is always equal to its \(K.E.\) \((b)\) Average potential and kinetic energy over any given time interval are always equal. \((c)\) Sum of the kinetic and potential energy at any point of time is constant. \((d)\) Average \(K.E.\) in one time period is equal to average potential energy in one time period. Choose the most appropriate option from the options given below: 2021 Medium
91. 91. Given below are two statements: Statement \(I :\) A second's pendulum has a time period of \(1\) second. Statement \(II :\) It takes precisely one second to move between the two extreme positions. In the light of the above statements, choose the correct answer from the options given below: 2021 Medium
92. 92. If the time period of a two meter long simple pendulum is \(2\, s\), the acceleration due to gravity at the place where pendulum is executing \(S.H.M.\) is 2021 Medium
93. 93. In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position. 2021 Medium
94. 94. In the given figure, a body of mass \(M\) is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant \(k,\) the frequency of oscillation of given body is :
    2021 Hard
95. 95. In the given figure, a mass \(M\) is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is \(k\). The mass oscillates on a frictionless surface with time period \(T\) and amplitude \(A\). When the mass is in equilibrium position, as shown in the figure, another mass \(m\) is gently fixed upon it. The new amplitude of oscillation will be
    2021 Medium
96. 96. In the reported figure, two bodies \(A\) and \(B\) of masses \(200\, {g}\) and \(800\, {g}\) are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be \(.....\,{rad} / {s}\) when \({k}=20 \,{N} / {m} .\)
    2021 Hard
97. 97. \({T}_{0}\) is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to \(\frac{1}{16}\) times of its initial value, the modified time 2021 Easy
98. 98. The function of time representing a simple harmonic motion with a period of \(\frac{\pi}{\omega}\) is : 2021 Hard
99. 99. The kinetic energy and potential energy of a particle executing simple harmonic motion will be equal, when displacement (amplitude = \(a\)) is 2021 Medium
100. 100. The motion of a mass on a spring, with spring constant \({K}\) is as shown in figure. The equation of motion is given by \(x(t)= A sin \omega t+ Bcos\omega t\) with \(\omega=\sqrt{\frac{K}{m}}\) Suppose that at time \(t=0\), the position of mass is \(x(0)\) and velocity \(v(0)\), then its displacement can also be represented as \(x(t)=C \cos (\omega t-\phi)\), where \(C\) and \(\phi\) are
     2021 Hard

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