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daveed
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can someone explain why when you have two physical pendula, one of which has a weight 2/3 of the way down falls at the same rate as one without a weight but is the same length?
The rod with the weight at 2/3 L can be approximated as a simple pendulum of length 2/3 L. The rod without the added weight cannot and must be treated as a physical pendulum (a uniform rod).daveed said:can someone explain why when you have two physical pendula, one of which has a weight 2/3 of the way down falls at the same rate as one without a weight but is the same length?
The masses of the pendula play a significant role in determining their motion. The heavier the mass, the slower the pendulum will swing. This is because the gravitational force acting on the mass increases with its weight, causing it to take longer to complete a swing.
The length of the pendula is directly proportional to their period, meaning that as the length of the pendula increases, the time it takes for one complete swing also increases. This relationship is known as the "Law of Periods" and was first discovered by Galileo Galilei.
The amplitude, or the maximum angle of swing, does not affect the period of the pendula. However, a larger amplitude will result in a longer distance traveled by the pendulum, causing it to take longer to complete one swing. This means that the amplitude indirectly affects the period of the pendula.
Yes, it is possible for two pendula with different lengths to have the same period. This occurs when the lengths of the pendula are in a specific ratio, known as the "Law of Lengths". For example, if the lengths of the pendula are in a ratio of 2:1, they will have the same period.
Pendula eventually come to a stop due to the presence of external factors such as friction and air resistance. These forces act on the pendulum and cause it to lose energy, leading to a decrease in its amplitude and eventually stopping its motion altogether.