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the period T of a rigid-body compound pendulum for small angles is given byT=2π√I/mgR

where I is the moment of inertia of the pendulum about the pivot point, m is the mass of the pendulum, and R is the distance between the pivot point and the center of mass of the pendulum.

For example, for a pendulum made of a rigid uniform rod of length L pivoted at its end, I = (1/3)mL2. The center of mass is located in the center of the rod, so R = L/2. Substituting these values into the above equation gives T = 2π√2L/3g. This shows that a rigid rod pendulum has the same period as a simple pendulum of 2/3 its length.

Q: How Can a compound pendulum be treated as a simple pendulum?

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A simple pendulum exhibits simple harmonic motion

A simple pendulum has one piece that swings. A complex pendulum has at least two swinging parts, attached end to end. A simple pendulum is extremely predictable, while a complex pendulum is virtually impossible to accurately predict.

applications of simple pendulum

The simple pendulum can be used to determine the acceleration due to gravity.

A simple pendulum.

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Compound pendulum is a physical pendulum whereas a simple pendulum is ideal pendulum. The difference is that in simple pendulum centre of mass and centre of oscillation are at the same distance.

Compound pendulum is a physical pendulum whereas a simple pendulum is ideal pendulum. The difference is that in simple pendulum centre of mass and centre of oscillation are at the same distance.

A simple pendulum exhibits simple harmonic motion

A simple pendulum has one piece that swings. A complex pendulum has at least two swinging parts, attached end to end. A simple pendulum is extremely predictable, while a complex pendulum is virtually impossible to accurately predict.

because in simple pendulum we say that we use a torsion less thread which of negligible mass but actually it's not negligible but in compound pendulum we don't such type of negligible materials hence it's better than the first one

The motion of the simple pendulum will be in simple harmonic if it is in oscillation.

applications of simple pendulum

The simple pendulum can be used to determine the acceleration due to gravity.

A simple pendulum.

simple pendulum center of mass and center of oscillation are at the same distance.coupled pendulum is having two bobs attached with a spring.

A simple pendulum is an idealized system. It's requirements like the bob should be a heavy particle, suspension string should be massless, perfectly inextensible etc. cannot be achieved perfectly. On the other hand a compound pendulum is a rigid body of any shape capable of vibrating about a horizontal axis passing through it(not through the centre of gravity), so it does not have such ideal conditions. Hence it can give more accurate result. ( I think this is the answer, may be there are other advantages also)

you can also use a simple pendulum to do it. your brain is full of problems if you cant do it by the easier wayForget thatgo on to this site and it gives you a method/procedure also go through www.phy.iitkgp.ernet.in/1styr/11-compound-pendulum.pdf