The degree of amplitude of a simple pendulum refers to the maximum angle the pendulum swings away from its equilibrium position. The restriction that the degree of amplitude should not exceed 5 is not a general rule for all pendulums, but it may be specific to a particular context or situation. Here are a few reasons why such a restriction could be in place:
Accuracy and linearity: When the amplitude of a simple pendulum exceeds a certain value, typically around 10 degrees, the motion of the pendulum is no longer linear. The period of the pendulum, which is the time it takes to complete one full swing, depends on the amplitude. For small amplitudes (usually less than 10 degrees), the period remains nearly constant, making the pendulum a reliable timekeeping device. However, as the amplitude increases, the period becomes dependent on the amplitude, which can introduce errors in timekeeping or other measurements.
Approximation of small angle: The simple pendulum equation, which describes the motion of a pendulum, is derived under the assumption that the angles involved are small. This approximation holds well for amplitudes up to around 10 degrees. When the amplitude exceeds this value, the approximation may no longer be accurate, and the equation may fail to predict the pendulum's behavior correctly.
Nonlinear effects: At larger amplitudes, the restoring force provided by gravity becomes nonlinear due to the sine function used in the equation of motion. This nonlinearity can introduce complex behaviors, such as multiple periods or chaotic motion, making the analysis more complicated. To maintain a simple and predictable motion, it is often preferred to keep the amplitude within a reasonable range.
It's important to note that the specific value of 5 degrees mentioned in your question is arbitrary and context-dependent. Different systems or experiments may have their own limitations based on factors such as accuracy requirements, equipment constraints, or the purpose of the study. Therefore, it's always essential to consider the specific context and requirements when determining the allowable degree of amplitude for a simple pendulum.