## OSCILLATIONS QUIZ - 1

JEE Advanced Physics Syllabus can be referred by the IIT aspirants to get a detailed list of all topics that are important in cracking the entrance examination. JEE Advanced syllabus for Physics has been designed in such a way that it offers very practical and application-based learning to further make it easier for students to understand every concept or topic by correlating it with day-to-day experiences. In comparison to the other two subjects, the syllabus of JEE Advanced for physics is developed in such a way so as to test the deep understanding and application of concepts..

Q1. A spring balance has a scale that can read from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance when displaced and released oscillates harmonically with a time period of 0.6 s. The mass of the body is (take )
•  10kg
•  25kg
•  18kg
•  22.8kg
Solution

Q2. Two particles P and Q describe SHM of same amplitude a and frequency v along the same straight line. The maximum distance between the two particles is. The initial phase difference between them is
•  0
•  ${\pi }{/}{2}$
•  ${\pi }{/}{6}$
•  ${\pi }{/}{3}$
Solution

Q3. A particle of mass m moving along the x -axis has a potential energy U(x) = a + bxwhere a and b are positive constants. It will execute simple harmonic motion with a frequency determined by the value of
•  b alone
•  b and a alone
•  b and m alone
•  b, a and m alone
Solution

Q4. The time taken by a particle executing simple harmonic motion to pass from point A to B where its velocities are same, is 2 s. After another 2 s, it returns to (b). The time period of oscillation is
•  2 s
•  4 s
•  6 s
•  8 s
Solution

Q5. A block is resting on a piston which executes simple harmonic motion in vertical plain with a period of 2.0 s in vertical plane at an amplitude just sufficient for the block to separate from the piston. The maximum velocity of the piston is
•  $\frac{{5/}}{{\pi }}{\mathrm{m}}{/}{\mathrm{s}}$
•  $\frac{{10/}}{{\pi }}{\mathrm{m}}{/}{\mathrm{s}}$
•  $\frac{{\mathrm{\pi /}}}{{2}}{\mathrm{m}}{/}{\mathrm{s}}$
•  $\frac{{20/}}{{\pi }}{\mathrm{m}}{/}{\mathrm{s}}$
Solution

Q6. A point mass is subjected to two simultaneous sinusoidal displacements in x - direction, and Adding a third sinusoidal displacement brings the mass to a complete rest. The values of B and ϕ
•
•
•
•
Solution

Q7. A particle executing SHM has velocities u and v and accelerations a and b in two of its positions. Find the distance between these two positions
•
•
•
•
Solution

Q8. Two masses m1 and m2 are suspended together by a massless spring of constant k. When the masses are in equilibrium, m1 is removed without disturbing the system; the amplitude of vibration is:
•
•  T
•
•
Solution

Q9. A metal rod of length L and mass m is pivoted at one end. A thin disk of mass M and radius R( < L) is attached at its centre to the free end of the rod. Consider two ways the disc is attached case A- the disc is not free to rotate about its centre and case B– the disc is free to rotate about its centre. The rod-disc system performs SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is/are true?
•  Restoring torque in case A = Restoring torque in case B
•  Restoring torque in case A < Restoring torque in case B
•  Angular frequency for case A < Angular frequency for case B
•  Angular frequency for case A  > Angular frequency for case B
Solution

Q10. A particle, free to move along the x-axis, has potential energy given by U(x) = K[ 1 - exp(-x2 ) for where k is a positive constant of appropriate dimensions. Then
•  For small displacement from x=0, the motion is simple harmonic
•  If its total mechanical energy is k/2 , it has its minimum kinetic energy at the origin
•  For any finite non-zero value of x, there is a force directed away from the origin
•  At points away from the origin, the particle is in unstable equilibrium
Solution

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