If one uses a tilt angleθ_0=20 deg., what is the difference between the periods given by Eq. 5 and Eq. 10?
If one uses a tilt angleθ_0=20 deg., what is the difference between the periods given by Eq. 5 and Eq. 10? (Use only the first two terms dependent on θ_0 in Eq. 5, i.e. neglect the higher terms).
T=2π√(l/g) (1+1/4 sin^2(θ_0/2)+ 9/64 sin^4 (θ_0/2)+⋯) (5)
T=2π√(l/g) (10)
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This period deviates from the simple pendulum period by 0.766859 percent. You can explore numbers t o convince yourself that the error in pendulum period is less than one percent for angular amplitudes less than 22 degrees.
22° 0.92925 %
25° 1.20289%
30° 1.740386 %
40° 3.131233 %
With Eq 10 the period T is bigger
Large Amplitude Pendulum
http://hyperphysics.phy-astr.gsu.edu/hbase/pendl.h...
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