As it turns out, a pendulum is a simple harmonic oscillator as well...its accele

Question

As it turns out, a pendulum is a simple harmonic oscillator as well...its acceleration is directly (negatively) proportional to its displacement from equilibrium. We'll actually do the physics of proving that in our next lecture. For now, some of the results in section 13.4 of you text will be useful. A man enters a tall tower, needing to know its height. He notes that a long pendulum extends from the ceiling almost to the floor and that its period is 10.5 s. (a) How tall is the tower? m (b) If this pendulum is taken to the Moon, where the free-fall acceleration is 1.67 m/s2 what is the period there? s

Explanation / Answer

You need to know the height of a tower, but darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor and that its period is 28 s. The acceleration of gravity is 9.81 m/s2 . How tall is the tower? The equation for the period of a pendulum : Time = 2 * p * (L/g)^0.5 L = length of pendulum in meters g = 9.81 m/s^2 28 = 2 * p * (L/9.81)^0.5 square both sides 28^2 = 4 * p^2 * L ÷ 9.81 multiply both sides by 9.81, and divide both sides by (4 * p^2) 28^2 * 9.81 ÷ (4 * p^2) = L solve for L

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