2. The period T of the ideal (no resistance) mathematical pendulum depends on the amplitude approximately as T = 2??(l/g) [1 + (?0^2)/16]. Here the angle (initial amplitude) must be measured in radians. ? radians = 180 degrees. Calculate periods for 5, 10, 20, 30 degrees and l = 25 cm, g = 980 cm/s^2. Calculate the period T0 as T0 = 2??(l/g) the first approximation (no amplitude dependence). Then find percent differences between the T0 and the periods for the angles above as %diff = |T0 ? T| / T0 × 100%.
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For 5 degrees: Convert 5 degrees to radians: 5 degrees * (π/180) = 5π/180 radians Calculate T: T = T0(1 + ((5π/180)^2)/16) For 10 degrees: Convert 10 degrees to radians: 10 degrees * (π/180) = 10π/180 radians Calculate T: T = T0(1 + ((10π/180)^2)/16) For 20 Show more…
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