It is said that Galileo discovered a basic principle of the pendulum - that the

Question

It is said that Galileo discovered a basic principle of the pendulum - that the period is independent of the amplitude - by using his pulse to time the period of swinging lamps in the cathedral as they swayed in the breeze. Suppose that one oscillation of a swinging lamp takes 4.0s. Part A How long is the lamp chain? Express your answer to two significant figures and include the appropriate units. Part B What maximum speed does the lamp have if its maximum angle from vertical is 3.0 degree ? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

we have T = 4.3sec p = 3.14 g = 9.80665m/s^2 using the equation T=2p v(L /g) T/2p = v(L /g) Square both sides,we get T^2/(2p)^2= L/g Multiply both sides by g,we get (T^2/(2p)^2)g = L now we have ((4.3^2sec^2)/(2*3.14)^2)*9.80665m/sec… =L (18.49sec^2/39.4384)*9.80665m/sec^2 =L 0.4688sec^2 * 9.80665m/sec^2 = L L= 4.62m ................................Answer

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