Introduction to Mechanical Vibrations. Ronald J. Anderson

the angle to 0.174533 radians. The percentage errors using the linear approximations are only 0.5% on the sine and 1.5% on the cosine. Ten degrees of rotation is a very large angle in the world of vibrations. We are typically looking at fractions of a degree where the linear approximations are very accurate.

      9 9 For those readers who already know about the standard form of these equations and are worried about the consequences of the term in square brackets being negative, I suggest you take time to consider what value must have for this term to be negative.

      10 10 All of the analysis here has assumed that the motion of the system can be described with a single degree of freedom and therefore a single equation of motion. We will soon see that this is not the case but that the material and methods presented here still apply.