What is the theory behind the compound pendulum? And why must it be released at a small angle ( 10 degrees)?

Small angle is used so you can use the approximation sin X=tan X and make math easier

massless string is used for the same reason (you should calculate an Integral using mass/length of the string etc)

Note also that the pendulum is frictionless (and we insist that physics describes the real world !!!)

Compound Pendulum Theory

The equation throughout a bob pendulum is: - t = 2??(l/g) for this reason, the era 't' relies upon on the dimensions 'l' of the pendulum and the acceleration of gravity 'g'. This equation is strictly valid purely for a small selection of angles of launch ((say) 0.a million to 30 levels). If the attitude of launch is somewhat super ((say) extra desirable than 30 levels) then the era of an easy bob pendulum does matter on the attitude of launch. In every day life, pendulums are constantly set to swing with a small perspective of launch - as an occasion, seen the pendulum interior a 'grandfather clock'.

I don't you what theory you are thinking of. Pendulums are usually described using classical mechanics.

The reason for the small angle is so that you can use the small angle approximation. This says that for small angles, sin(x) is approximately equal to tan(x). This greatly simplifies the math making it a lot easier to do. However, in more advance physics classes, the small angle approximation is not always used.