The error due to approximation can be estimated as
For 5 degree, the error is about which is a very small error.
For 10 degree, the error is about 4*0.127%= 0.50%
For 20 degree, the error is about 16*0.127=2.0%
What I want to point out is:
1. 5 degree is not a magic number: user should provide the precission required in order to determined the maximum angle for good approximation.
2. Even 20 degree only produce 2% of error which is normally smaller than experiment error when student perform real experiment.
The solution for RLC circuit is:
Because is independent of charge or current: i.e. damping rate is the same for the same R/L value.
You should be able to find out solution for pendulum(compare equations for RLC and pendumum set)