- #1
particlemania
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Homework Statement
Is Time Period = \int \frac{1}{v} dx ??
If yes, the under what limits of integration??
Time Period: Limits of Integration?
- Thread starter particlemania
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SUMMARY
The discussion centers on the relationship between time period and velocity in the context of calculus. The integral expression for time period is confirmed as Time Period = ∫ (1/v) dx, where v = dx/dt. It is established that this integral is valid for any limits of integration as long as velocity is non-zero. The conversation also touches on scenarios where velocity may approach zero, prompting further exploration of the implications.
- Understanding of calculus, specifically integration techniques.
- Familiarity with the concept of velocity as
v = dx/dt. - Knowledge of limits of integration in definite integrals.
- Basic principles of physics related to motion and time.
- Explore the implications of integrating with zero velocity in physics problems.
- Study the application of definite integrals in calculating time periods for various motion scenarios.
- Learn about the relationship between velocity and displacement in calculus.
- Investigate advanced integration techniques for non-standard velocity functions.
Students and professionals in physics and mathematics, particularly those studying motion, calculus, and integration techniques.
Is Time Period = \int \frac{1}{v} dx ??
If yes, the under what limits of integration??
- #2
fluidistic
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particlemania said:
Could you please provide more information? What problem are you solving?
- #3
tiny-tim
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Hi particlemania! 
If x is a function only of t, and if v = dx/dt, and is non-zero, then yes ∫ dx/v = ∫ (dt/dx)dx = ∫ dt, and this should work for any limits.
If v = 0 at some point, it may still work … what do you think?
particlemania said:
If x is a function only of t, and if v = dx/dt, and is non-zero, then yes ∫ dx/v = ∫ (dt/dx)dx = ∫ dt, and this should work for any limits.
If v = 0 at some point, it may still work … what do you think?
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