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The popular formula for the period of a pendulum works only for small angular displacements. In deriving it, you need to assume that theta, the angular displacement from the vertical, measured in radians, is equal to sin(theta). If not, you need to make much more complicated calculations. There are also other assumptions to simplify the formula - eg string is weightless.
The swing of the pendulum will precess with the rotation of the earth. This may not work if the pendulum hits its stand! See Foucault's Pendulum (see link).
The motion of the pendulum will die out as a result of air resistance.
Thermal expansion can change the length of the pendulum and so its period.
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What is a limitations to a simple pendulum?
One limitation of a simple pendulum is that it assumes the string or rod to be massless and rigid, which may not always be the case in real-world situations. Additionally, the simple pendulum formula assumes small amplitudes of swing, so it may not accurately predict the behavior of large swings. Friction and air resistance can also affect the motion of a simple pendulum, introducing further limitations.
Why a compound pendulum is called equivalent simple pendulum?
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.
Why a compound pendulum is called an equivalent simple pendulum?
A compound pendulum is called an equivalent simple pendulum because its motion can be approximated as that of a simple pendulum with the same period. This simplification allows for easier analysis and calculation of its behavior.
Differences between compound pendulum and simple pendulum?
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.
When will the motion of simple pendulum be shm?
The motion of a simple pendulum will be simple harmonic when the angle of displacement from the vertical is small (less than 10 degrees) and the amplitude is also small.
