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A block of mass ‘m‘ is attached to a spring in natural length of spring constant ‘k*., The other end A of the spring is moved with a constant velocity v away from the block, . Find the maximum extension in the spring., , Be", , {mv2 2, = "Iw?, oi 2m, , Asystem is shown in the figure. The time period for small oscillations of the two blocks, will be., , , , , , m ‘ rs nm, , TEN MTTUTTe TNT NTN ENT, , , , , , , , , , , , , , , , , , , , , , , , , , k 2, nm nm, [3m [am am [3m, (A) 2x yr (B) 2% 3 (C)2n ak (D) 2x 8k, , Two particles P and Q describe S.H.M. of same amplitude a, same frequency f along, the same straight line from the same mean positon. The maximum distance between, , the two particles is a V2 . The phase difference between the particle is:, , (A) zero (B) w2 (C) x/6 (D) w/3, The time taken by a particle performing SHM on a straight line to pass from pointAto B, where its velocities are same is 2 seconds. After another 2 seconds it returns to B. The, time period of oscillation is (in seconds):, , (A)2 (B)4 (C)6 (D)8
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Aparticle performs S.H.M. on x-axis with amplitude A and time period T. The time, taken by the particle to travel a distance A/5 starting from rest is:, , Tt T (4) T ) T (), (A) = B)— cos '|— C)— cos '| — D)— sin "| —, ) 29 ( ae (5] ( = ( ( ae (3, Arod of length ¢ is in motion such that its ends A and B are moving along x-axis and, , y-axis respectively. Itis given that ; = 2 rad/s always. P is a fixed point on the rod., Let M be the projection of P on x-axis. For the time interval in which 6 changes from, , Oto = choose the correct statement,, , , , (A) The acceleration of Mis always directed towards right, (B) M executes SHM, , (C) M moves with constant speed, , (D) M moves with constant acceleration, , The coefficient of friction between blocks of mass m and 2m is ,: = 2 tan 6. There is no, friction between block of mass 2m and inclined plane. The maximum amplitude of two, block system for which there is no relative motion between the blocks., , , , [kK, m, , (A) g sine \, , (By masine (c) 79822 (D) None of these
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10, , Ablock of mass ‘m’ is suspended from a spring and executes vertical SHM of time, period T as shown in figure. The amplitude of the SHM is Aand spring is never in, compressed state during the oscillation. The magnitude of minimum force exerted by, spring on the block is, , 2 2 2 2, (A) mg- ma (B) ma+ ma (C) mg- = ma (D) ma+ ma, , Graph shows the x(t) curves for three experiments involving a particular spring- block, system oscillating in SHM. The kinetic energy of the system is maximum att = 4 sec., for the situation :, , , , tin sec), , , , , , , , , , , , , , (A)1 (B)2 (C)3 (D) Same in all, Aparticle performs S.H.M. of amplitude A along a straight line. When itis ata, , distance s A from mean position, its kinetic energy gets increased by an, , 1 . . ., amount . ma? A’ due to an impulsive force. Then its new amplitude becomes:, , aye A a (C)V2A (0) SA
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11. Ahorizontal spring—block system of mass 2kg executes S.H.M. When the block is, passing through its equilibrium position, an object of mass 1kg is put on it and the, two move together. The new amplitude of vibration is (A being its initial amplitude):, , > iy *, (a) {5A ®) 54 (0) 2A 0), , 12. Apendulum of length L and bob of mass M has a spring of force constant k connected horizontally to it at a distance h below its point of suspension. The rod is in, equilibrium in vertical position. The rod of length L used for vertical suspension is, rigid and massless. The frequency of vibration of the system for small values of 6 is, , , , , , , , , , , , “4 kh 1 [mgl+k me (kh?, (A) 5 fou (a0) m (C) 2m kh ©) acyl 'n, , 13 Ametre stick swinging in vertical plane about a fixed horizontal axis passing, through its one end undergoes small oscillation of frequency f,. Ifthe bottom half of, the stick is cut off, then its new frequency of small oscillation would become:, , (A), (8) vat, (C)2f, (0) 22,
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14, , 15, , Astraight rod of negligible mass is mounted on a frictionless pivot and masses 2.5 kg, and 1 kg are suspended at distances 40 cm and 100 cm respectively from the pivot as, shown. The rod is held at an angle 6 with the horizontal and released., , (A), (B), (C), , (D), , , , , , The rod executes periodic motion about horizontal position after the release., The rod remains stationary after the release., The rod comes to rest in vertical position with 2.5 kg mass at the lowest point, , The rod executes periodic motion about vertical position after the release., , Aparticle of mass m = 2 kg executes SHM in xy-plane between points Aand B as shown, in figure, under action of force F = F,i + F,j . Minimum time taken by particle to move from, Ato Bis 1 sec. Att = 0 the particle is at x = 2 and y = 2. Then F_ as function of time tis, , y, , ‘A(2, 2), x, 6, (2-2), (A) —4n? sin xt (B) —4n? cos xt, ( C) 4x? cos rt (D) None of these
