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:

where

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)