Key on a string: double pendulum & consequences of not using a bob on a string? While trying to do an at home experiment about a single pendulum, I used a key on a rope and let it swing. I came to the conclusion that this could not be a single pendulum, because of the extra 'point of rotation', where the key was attached to the string. Does this hold true? Is it a double pendulum, and what are the consequences of not using a more traditional setup, where a point mass is suspended from the string?
 A: If the length of the string is much greater than the length of the key then it can be modelled fairly accurately by the equations for a simple pendulum in most situations. If the length of the string is comparable to the length of the key then it can be modelled fairly accurately by the equations for a rigid double pendulum in most situations (so long as the differences in mass/unit-length for the string and key are taken into account).
But my caveat of 'most situations' is because both the simple pendulum and double pendulum equations are only approximations to reality. Even if you remove 'side-effects' such as mass and elasticity of the string, air resistance, and finite mass distribution within the bob by using a very thin inelastic string, a small dense bob (as a true point mass doesn't exist in reality), and operate in a vacuum, the actual motion of the pendulum will not be perfect harmonic motion because the restoring force on the bob (as a function of angular displacement $theta$) is proportional to $sin(theta)$ rather than to $theta$ - and harmonic motion is only an approximation to that. In practice, there is no analytic solution to the motion of any pendulum except in the limit where maximum displacement tends to zero.
Conclusion is, physics in reality can be complicated.
