BOOXX XXX a I III b II III c I IV d II IV 59 When the displacement of a particle executing SHM is one fourth of its amplitude what fraction of the total energy is the kinetic energy 3 a 16 15 b 60 A block whose mass is 1 kg is fastened to a spring The spring has a spring constant of 100 Nm The block is pulled to a distance x 10 cm from its equilibrium position at x 0 on a frictionless surface from rest at t 0 The kinetic energy and potential energy of the block when it is 5 cm away from the mean position is a 0 0375 J 0 125 J b 0 125 1 0 375 J c 0 125 J 0 125 J d 0 375 J 0 375 c 2 SOME SYSTEMS EXECUTING SIMPLE HARMONIC MOTION 61 A body of mass m is situated in a potential field U x U 1 cosax where U and a are constants The time period of small oscillations is b 2 a 2 15 16 771 U m 200 771 U a 2m U a d 2n 62 The frequency of oscillations of a mass m suspended by a spring is u If the length of the spring is cut to one half the same mass oscillates with frequency U The value v v is a 2 b 2 65 In the question number 64 the maxim acceleration of the collar is b 10 ms d 20 m s a 5 ms c 15 m s 2 b 12 s c 36 s d 72 s 64 A 5 kg collar is attached to a spring of spring constant 500 N m It slides without friction over a horizontal rod The collar is displaced from its equilibrium position by 10 cm and released The time period of oscillation is 66 to a spring of spring A body of mass 20 g connected constant k executes simple harmonic motion with frequency of 5 m Hz The value of spring consta a 4 Nm b 3 Nm c 2 Nm d 5Nm 67 Two blocks each of mass m is connected to the spring of spring constant k as shown in the figure 191 in opposite If the blocks are displaced slightly directions and released they will execute simp harmonic motion The time period of oscillation m a 21 b 2x a T 2 m c T 2 000000 Ba mV mB Va a 0 5 m s c 2 ms m 2k 68 An air chamber of volume V has a neck of crow sectional area a into which a light ball of mass just fits and can move up and down without friction The diameter of the ball is equal to that of the ne of the chamber The ball is pressed down a little and released If the bulk modulus of air is B the time period of the oscillation of the ball is b T 2n c 2 m 4k d T 2n 600 Nm 43kg 600 Nm 000000 000000 27x d 2 b 1 ms d 3 ms BV ma 69 A spring balance has a scale that reads from 0 50 kg The length of the scale is 20 cm A block of mass m is suspended from this balance when displaced and released it oscillates with a period 0 5 s The value of m is Take g 10 ms a 8 kg b 12 kg c 16 kg d 20 kg c 4 d 3 63 Time period of oscillation of a spring is 12 s on 70 A trolley of mass 3 kg as shown in figure is earth What shall be the time period if it is taken to moon connected to two identical springs each of spring constant 600 N m If the trolley is displaced from its equilibrium position by 5 cm and released the maximum speed of the trolley is a 6 s mV Ba