A pendulum that moves through its equilibrium position once every 1.000 s is som

Question

A pendulum that moves through its equilibrium position once every 1.000 s is sometimes called a seconds pendulum. (a) What is the period of any seconds pendulum? s (b) In Cambridge, England, a seconds pendulum is 0.9942 m long. What is the free-fall acceleration in Cambridge? (Use 4 significant figures in your answer.) WebAssign will check your answer for the correct number of significant figures. m/s2 (c) In Tokyo, Japan, a seconds pendulum is 0.99274 m long. What is the free fall acceleration in Tokyo, Japan? (Use 5 significant figures in your answer.) WebAssign will check your answer for the correct number of significant figures. m/s2

Explanation / Answer

a) The phrase 'moves through its equilibrium position once every 1.000 sec' means that its PERIOD, T is actually 2 sec, as it passes through equilibrium twice per period. From the formula for a simple pendulum,

T = 2(L/g) g = 4²L/T² where T = 2.000. Finally,

g = ²*L

b) g = 9.8123 m/s^2

c) g = 9.7979 m/s^2

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