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Time period of a particle in SHM depends...

Time period of a particle in `SHM` depends on the force constant `k` and mass `m` of the particle `T = 2psqrt((m)/(k))`. A simple pendulum exeutes `SHM` approximately. Why then is the period of a pendulum independent of the mass of the pendulum ?

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The correct Answer is:
(a) For a simple pendulum, `k` itself is propotinal to `m`, so `m` cancels out.
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Answer the following questions: (a) Time period of particle is S.H.M. depends on the force constant k and mass m of the particle : T=2pisqrt(m//k). A simple pendulum executes S.H.M. approximately. Why then is the time-period of a pendulum independent of the mass of the pendulum? (b) The motino of simple pendulum is approximatley simple harmonic for small angles of oscillation. For large angle of oscillation, a more involved analysis (beyond the scope of this book) shows that T is greater that 2pisqrt(l//g) . Think of a quanlitative argument to appreciate this result. (c) A man with a wrist watch on his hand falls from the top of tower. Does the watch give correct time during the free fall? (d) What is teh frequency of oscillation of a simple pendulum mounted iin a cabin that is freely falling under gravity?

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RESONANCE-SIMPLE HARMONIC MOTION -Board Level Exercise
  1. Define amplitude of S.H.M. ?

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  2. Why the motion of a satellite around a planet cannot be taken as S.H.M...

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  3. Is oscillation of a mass suspended by a spring simple harmonic ?

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  4. Which of the following examples represent (nearly) simple harmonic mot...

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  5. Fill in the blanks using appropriate word from the list at the end of ...

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  6. A restoring force is a must for a body to execute S.H.M Explain, why

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  7. A man is standing on a platform moving up and down as a S.H.M. will th...

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  8. An air chamber of volume V has a neck area of cross section A into whi...

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  9. Show that for a particle in linear S.H.M., the average kinetic energy ...

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  10. A man with a wrist watch on his hands fall from the top of a tower. Do...

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  11. Time period of a particle in SHM depends on the force constant k and m...

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  12. Figure a) shows a spring of force constant k clamped rigidly at once e...

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  13. What is a simple pendulum? Find an expression for the time period and ...

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  14. Answer the following questions: (a) The motion of a simple pendulum ...

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  15. A simple pendulum of length l and having a bob of mass M is suspended ...

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  16. Define resonance.

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  17. Define forced and resonant vibrations

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  18. What are undamped and damped oscillations ?

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  19. Derive the expression for equivalent spring constant of (i) parallel...

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  20. Find equivalent spring constant for the system:

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