How long does it take for the pendulum to swing to the opposite side?

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SUMMARY

The discussion revolves around calculating the time it takes for a pendulum to swing from an initial angle of 8.8° to 4.4° on the opposite side. The formula used for the period of a pendulum is T = 2π√(L/g), where L is the length of the string (1.0 m) and g is the acceleration due to gravity (9.81 m/s²). The correct approach indicates that the time taken to reach 4.4° is 3T/4, as the pendulum's motion is not linear and involves harmonic motion principles. The user expresses confusion regarding the time calculations and the reasoning behind the 3T/4 conclusion.

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  • Understanding of pendulum motion and harmonic oscillators
  • Familiarity with the formula for the period of a pendulum (T = 2π√(L/g))
  • Basic knowledge of angular displacement and its relation to pendulum motion
  • Concept of average speed in oscillatory motion
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  • Study the principles of harmonic motion in pendulums
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Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify pendulum dynamics.

drifter8027
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Homework Statement



I searched and got nothing, I am also new here as my friend recently introduced me to this forum last night. I have gotten every single problem correct except this one so here goes:

A 300 g mass on a 1.0 m long string is pulled 8.8° to one side and released. How long does it take for the pendulum to reach 4.4° on the opposite side?

I only have one more try or else i lose all my credit (webassign ah) but any help is appreciated. Thank you!

Homework Equations



T = 2*pi*sqrt(L/g)
3T/4 = answer

The Attempt at a Solution



T= 2*pi*sqrt(1.0/9.81)
 
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Why do you say 3T/4 is the answer? From a rational standpoint, it will take less than T/2 to get to 4.4 degrees - its halfway point - since its average speed is greater than going from 4.4 to 8.8 degrees...it will take T/4 to get to equilibrium from its initial position., for sure, but from there you can't use ratios.
 
Yeah I suppose that my submission really doesn't make sense at all. But it was my last problem it's been a long day.
 

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