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Q13. Oscillatory Motion Q14. Wave Motion

Explore the fundamentals of oscillatory and wave motion, including amplitude variations, energy principles, harmonic motion, and wave interactions. Understand key concepts through detailed explanations and practice questions.

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Q13. Oscillatory Motion Q14. Wave Motion

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  1. Q13. Oscillatory MotionQ14. Wave Motion

  2. Two identical undamped oscillators have the same amplitude of oscillation only if they are started with the same : • displacement x0 • velocity v0 • phase • 2 x02 v02 • x02 2v02

  3.  same A requires same E. • displacement x0 • velocity v0 • phase • 2 x02 v02 • x02 2v02 Different v0 gives different A. Different x0 gives different A. A is indifferent to phase. Same E gives same A. Sum is meaningless.

  4. The amplitude of any oscillator can be doubled by: : • doubling only the initial displacement • doubling only the initial speed • doubling the initial displacement and halving the initial speed • doubling the initial speed and halving the initial displacement • doubling both the initial displacement and the initial speed

  5. • doubling only the initial displacement • doubling only the initial speed • doubling the initial displacement and halving the initial speed • doubling the initial speed and halving the initial displacement • doubling both the initial displacement and the initial speed

  6. A certain spring elongates 9 mm when it is suspended vertically and a block of mass M is hung on it. The natural frequency of this mass-spring system is : • is 0.088 rad/s • is 33 rad/s • is 200 rad/s • is 1140 rad/s • cannot be computed unless the value of M is given

  8. A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm. When it is at x = x1, its kinetic energy is K = 5J and its potential energy (measured with U = 0 at x = 0) is U = 3J. When it is at x = –1/2xm, the kinetic and potential energies are : • K = 2J and U = 6J • K = 6J and U = 2J • K = 2J and U = – 6J • K = 6J and U = – 2J • K = 5 and U = 3J

  9. Five hoops are each pivoted at a point on the rim and allowed to swing as physical pendulums. The masses and radii are : Order the hoops according to the periods of their motions, smallest to largest. • 1, 2, 3, 4, 5 • 5, 4, 3, 2, 1 • 1, 2, 3, 5, 4 • 1, 2, 5, 4, 3 • 5, 4, 1, 2, 3

  10. Five hoops are each pivoted at a point on the rim and allowed to swing as physical pendulums. The masses and radii are : Order the hoops according to the periods of their motions, smallest to largest. • 1, 2, 3, 4, 5 • 5, 4, 3, 2, 1 • 1, 2, 3, 5, 4 • 1, 2, 5, 4, 3 • 5, 4, 1, 2, 3 R  For small  : 

  11. The displacement of a string carrying a traveling sinusoidal wave is given by At time t  0 the point at x 0 has velocity v0 and displacement y0. The phase constant  is given by tan   : v0 /w y0 w y0 / v0 w v0 / y0 y0 / w v0 w v0 y0

  12. The displacement of a string carrying a traveling sinusoidal wave is given by At time t  0 the point at x 0 has velocity v0 and displacement y0. The phase constant  is given by tan   :

  13. The diagram shows three identical strings that have been put under tension by suspending masses of 5 kg each. For which is the wave speed the greatest ? • 1 • 2 • 3 • 1 and 3 tie • 2 and 3 tie

  14.  Larger T  larger v Ans: 1 & 3 tied

  15. Suppose the maximum speed of a string carrying a sinusoidal wave is vs. When the displacement of a point on the string is half its maximum, the speed of the point is : • vs/ 2 • 2 vs • vs / 4 • 3 vs / 4 • 3 vs / 2

  16. Suppose the maximum speed of a string carrying a sinusoidal wave is vs. When the displacement of a point on the string is half its maximum, the speed of the point is :  

  17. The sinusoidal wave y(x,t) ym sin( k x –  t ) is incident on the fixed end of a string at xL. The reflected wave is given by : ym sin( k x + w t ) –ym sin( k x + w t ) ym sin( k x + w t – k L ) ym sin( k x + w t – 2 k L ) –ym sin( k x + w t + 2 k L )

  18. The sinusoidal wave y(x,t) ym sin( k x –  t ) is incident on the fixed end of a string at xL. The reflected wave is given by : Let the time of incidence be t0 

  19. Standing waves are produced by the interference of two traveling sinusoidal waves, each of frequency 100 Hz. The distance from the 2nd node to the 5th node is 60 cm. The wavelength of each of the two original waves is : • 50 cm • 40 cm • 30 cm • 20 cm • 15 cm

  20. Standing waves are produced by the interference of two traveling sinusoidal waves, each of frequency 100 Hz. The distance from the 2nd node to the 5th node is 60 cm. The wavelength of each of the two original waves is : In order to have a standing wave, these waves must travel in opposite directions. Distance from the 2nd node to the 5th node is 60 cm : 

  21. A 40-cm long string, with one end clamped and the other free to move transversely, is vibrating in its fundamental standing wave mode. If the wave speed is 320 cm/s, the frequency is : • 32 Hz • 16 Hz • 8 Hz • 4 Hz • 2 Hz

  22. A 40-cm long string, with one end clamped and the other free to move transversely, is vibrating in its fundamental standing wave mode. If the wave speed is 320 cm/s, the frequency is : One end clamped and the other free to move transversely. Fundamental standing wave mode   4 L.

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