How long must the pendulum in a grandfather clock be so that it takes 1 second to

  • Thread starter Thread starter Antonio™
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Antonio™

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swing from left to right? I professor told me it was a trick question...i have no idea what the answer is...
 
A swing from left to right is only half a complete cycle ... the complete cycle is a swing from left to right, and back left again. This means the pendulum has a period of 2 seconds, not 1. That's the trick.

The period and the length of a pendulum are related by the equation
T = 2π√(L/g) and squaring both sides yields

T² = 2²π²L/g

T² = 4π²L/g
gT² = 4π²L
L = gT²/4π²

L = 9.8*2²/4π² = 9.8/π² = 0.99 m which is close to 1 m.
 
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