09%20-%20Oscillations

09%20-%20Oscillations - 09 - OSCILLATIONS Page 1 ( Answers...

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09 - OSCILLATIONS Page 1 ( Answers at the end of all questions ) 1 ) Two simple harmonic motions are represented by the equations y 1 = 0.1 sin ( 100 π t + π / 3 ) and y 2 = 0.1 cos π t. The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is ( a ) π / 3 ( b ) - π / 6 ( c ) π / 6 ( d ) - π / 3 [ AIEEE 2005 ] 2 ) The function sin 2 ( ω t ) represents ( a ) a periodic, but not simple harmonic, motion with a period π / ω ( b ) a periodic, but not simple harmonic, motion with a period of 2 π / ω ( c ) a simple harmonic motion with a period π / ω ( d ) a simple harmonic motion with a period 2 π / ω [ AIEEE 2005 ] 3 ) The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hall near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time-period of the oscillation would ( a ) first decrease and then increase to the original value ( b ) first increase and then decrease to the original value ( c ) increase towards a saturation value ( d ) remain unchanged [ AIEEE 2005 ] 4 ) If a simple harmonic motion is represented by 0 x α dt x d 2 2 = + , its time period is ( a ) α π 2 ( b ) α π 2 ( c ) α π 2 ( d ) 2 π α [ AIEEE 2005 ] 5 ) The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is t 0 in air. Neglecting frictional force of water and given that the density of the bob is ( 4 / 3 ) × 1000 kg / m 3 , what relationship between t and t 0 is true ? ( a ) t = t 0 ( b ) t = t 0 / 2 ( c ) t = 2 t 0 ( d ) t = 4 t 0 [ AIEEE 2004 ] 6 ) A particle at the end of a spring executes simple harmonic motion with a period t 1, while the corresponding period for another spring is t 2 . If the period of oscillation with the two springs in series is T, then ( a ) T = t 1 + t 2 ( b ) T 2 = t 1 2 + t 2 2 ( c ) T - 1 = t 1 - 1 + t 2 - 1 ( d ) T - 2 = t 1 - 2 + t 2 - 2 [ AIEEE 2004 ] 7 ) The total energy of a particle executing simple harmonic motion ( a ) x ( b ) x 2 ( c ) is independent of x ( d ) x where x is the displacement from the mean position. [ AIEEE 2004 ] 8 ) A particle of mass m is attached to a spring ( of spring constant k ) and has a natural angular frequency of ω 0 . An external force F ( t ) proportional to cos ω t ( ω ω 0 ) is applied to the oscillator. The time displacement of the oscillator will be proportional to ( a ) m / ( ω 0 2 - ω 2 ) ( b ) F t / m( ω 0 2 - ω 2 ) ( c ) 1 / m( ω 0 2 - ω 2 ) ( d ) m / ( ω 0 2 + ω 2 ) [ AIEEE 2004 ]
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09 - OSCILLATIONS Page 2 ( Answers at the end of all questions ) 9 ) In forced oscillation of a particle, if the amplitude is maximum for a frequency ω 1 of the force while the energy is maximum for a frequency ω 2 of the force, then ( a ) ω 1 = ω 2 ( b ) ω 1 > ω 2 ( c ) ω 1 < ω 2 ( d ) ω 1 < ω 2 when damping is small and ω 1 > ω 2 when damping is large [ AIEEE 2004] 10 ) The displacement
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09%20-%20Oscillations - 09 - OSCILLATIONS Page 1 ( Answers...

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