What is time average of tension?

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SUMMARY

The discussion centers on calculating the time average of tension in a simple pendulum undergoing small oscillations. The key equation presented is T = mgcosθ - mv²/L, where T represents tension, m is mass, g is gravitational acceleration, v is velocity, and L is the length of the pendulum. The contributor seeks guidance on determining the angle θ as a function of time to compute the average tension compared to mg. A suggestion is made to consider the tension when the pendulum is at rest to simplify the problem.

PREREQUISITES
  • Understanding of simple harmonic motion and pendulum dynamics
  • Familiarity with the concepts of tension and gravitational force
  • Knowledge of calculus, specifically averaging functions
  • Basic physics principles related to force balance in pendulums
NEXT STEPS
  • Study the derivation of tension in a simple pendulum using force balance equations
  • Learn how to express angular displacement θ as a function of time for small oscillations
  • Explore the concept of time averages in oscillatory motion
  • Investigate the effects of varying amplitudes on tension in pendulum systems
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Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to enhance their understanding of pendulum dynamics.

lemon__meringue
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Summary: My homework question asks: Consider a simple pendulum, undergoing small oscillations. Is the time average of the tension in the string of the pendulum larger or smaller than mg? By how much?

My homework question asks: Consider a simple pendulum, undergoing small oscillations. Is the time average of the tension in the string of the pendulum larger or smaller than mg? By how much?

I tried to use T= mgcosθ - mv^2/L to find the angle in terms of time and then use the average of a function things which I learned in calc. But I have no idea how to go about finding θ (t) . Is this right thought the process? or is there a better way? Please help me :'(

Thanks for any help in advance
 
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Welcome to PF. I moved it to a homework help forum. Next time you have a homework problem, post it in the homework forum and fill out the template the forum will provide.

Here's a hint. How much is the tension if the small oscillations are zero in size? In other words, standing still.
 
You find theta as a function of time by solving the force balance in the tangential direction.
 

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