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Can every oscillatory motion be treated ...

Can every oscillatory motion be treated as SHM in the limit of small amplitude?

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No, not at all. In the limit of small amplitude only those oscillatory motion can be treated as simple harmonic for which the restoring force (or torque) becomes linear.
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FIITJEE-SIMPLE HARMONIC MOTION-Exercise
  1. Can a motion be oscillatory but not simple harmonic? If your answer is...

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  2. Can every oscillatory motion be treated as SHM in the limit of small a...

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  3. Can a body have acceleration without having velocity?

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  4. Determine whether or not the following quantities can be in the same d...

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  5. Determine whether or not the following quantities can be in the same d...

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  6. Determine whether or not the following quantities can be in the same d...

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  7. Which of the following relationship between the force F on a particle'...

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  8. How are each of the following quantities of a SHM affected by doubling...

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  9. How are each of the following quantities of a SHM affected by doubling...

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  10. How are each of the following quantities of a SHM affected by doubling...

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  11. How are each of the following quantities of a SHM affected by doubling...

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  12. What is the frequency of the K.E. and total energy of a body in S.H.M...

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  13. How will the frequency of small oscillation of a simple pendulum chang...

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  14. How will the frequency of small oscillation of a simple pendulum chang...

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  15. How will the frequency of small oscillation of a simple pendulum chang...

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  16. How will the frequency of small oscillation of a simple pendulum chang...

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  17. At what point in the motion of a simple pendulum is the string tension...

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  18. Find the time period of a simple pendulum in a carriage accelerating ...

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  19. Find the time period of a simple pendulum in a carriage accelerating ...

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  20. A hollow metal sphere is filled with water and a small hole is made at...

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