Suppose that we have a pendulum of length l and attached mass m. Now suppose we

Question

Suppose that we have a pendulum of length l and attached mass m. Now suppose we also have a similar pendulum with length 4l, and we decide to measure the periods of oscillation of each denoted Tl and T4l. For small oscillations what is the ratio of: (a) T4l to Tl? (b) 4l to l? Suppose that we have a pendulum of length l and attached mass m. Now suppose we also have a similar pendulum with length 4l, and we decide to measure the periods of oscillation of each denoted Tl and T4l. For small oscillations what is the ratio of: (a) T4l to Tl? (b) 4l to l? Suppose that we have a pendulum of length l and attached mass m. Now suppose we also have a similar pendulum with length 4l, and we decide to measure the periods of oscillation of each denoted Tl and T4l. For small oscillations what is the ratio of: (a) T4l to Tl? (b) 4l to l?

Explanation / Answer

The formula for time period of simple pendilum is

T = 2pi sqr l/g

for lenght l

Tl = 2pi sqrt l/g

for 4l

T41 = 2pi sqrt 4l/g

take ratio T4l to Tl

T4l/ T1 = 2pi sqrt 4l/g/2pi sqrt l/g

          =sqrt 4l/l

         = sqrt 4

T4l/ Tl = 2

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= 2pi/T

for l = 2pi/Tl = 2pi/2pi sqrt l/g

for 4l = 2 pi/ T4l = 2pi/2pi sqrt 4l/g

take the ration 4l /l =2pi/2pi sqrt 4l/g/2pi/2pi sqrt l/g = sqr l/4l = 0.5

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