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While noting the time period of a simple pendulum amplitude of vibration should be kept- A) reasonably large for easy measurements B)as small as possible C) reasonably constant D) very large as the value of t is very large?
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Introduction:
The amplitude of vibration refers to the maximum displacement of a simple pendulum from its equilibrium position. It is an important parameter that affects the behavior and characteristics of the pendulum's motion. The time period of a simple pendulum is the time taken for one complete oscillation.

Reasonably large amplitude for easy measurements:
A) Reasonably large amplitude of vibration should be kept for easy measurements. This is because when the amplitude is larger, the displacement of the pendulum is more noticeable and easier to measure accurately. If the amplitude is too small, it becomes difficult to measure the displacement precisely, leading to errors in the measurement of the time period.

Small amplitude:
B) The amplitude of vibration should not be kept as small as possible. If the amplitude is too small, the pendulum's motion becomes closer to simple harmonic motion, where the restoring force is directly proportional to the displacement. In this case, the time period of the pendulum becomes independent of the amplitude, and the pendulum behaves like an ideal simple harmonic oscillator. However, in real-world situations, the amplitude cannot be reduced to zero, and there will always be some deviation from simple harmonic motion due to factors like air resistance and friction. Therefore, keeping the amplitude reasonably large allows us to observe and analyze the effects of these factors on the pendulum's motion.

Reasonably constant amplitude:
C) The amplitude of vibration should be kept reasonably constant. This ensures that the pendulum's motion remains predictable and reproducible. If the amplitude varies significantly during the oscillation, the time period may change, making it difficult to obtain accurate measurements. By maintaining a constant amplitude, the pendulum's motion can be more accurately described by the laws of physics, allowing for precise calculations and comparisons.

Large amplitude for very large value of t:
D) The amplitude of vibration does not need to be very large for a pendulum with a very large value of t (time period). The time period of a simple pendulum is determined primarily by the length of the pendulum and the acceleration due to gravity. It is independent of the amplitude as long as the amplitude is reasonably small. Therefore, increasing the amplitude to a very large value does not significantly affect the time period for a pendulum with a large value of t.

Conclusion:
In conclusion, for a simple pendulum, the amplitude of vibration should be reasonably large for easy measurements and reasonably constant to ensure predictable and reproducible motion. Keeping the amplitude reasonably small allows us to observe the effects of external factors on the pendulum's motion. However, for a pendulum with a very large time period, the amplitude does not need to be very large as it does not significantly affect the time period.
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Attempt All sub parts from each question.Galileo’s Isochronous Pendulum: Galileo observed a lamp swinging from ceiling at Pisa cathedral ceiling. He was the first scientist to observe how long it took any object suspended from a rope or chain (a pendulum) to swing back and forth. There were no wrist watches at that time, so Galileo used his own pulse as a time measurement. Galileo observed that no matter how big the swings were, as in when the lamp was first swung, to how small the swings were as the lamp returned to a standstill, the time it took for each swing to complete was exactly the same. So, he concluded that the oscillations are isochronous. Anyhow, it was proved by advanced experimentation that the isochronism of simple pendulum is correct within 1% under the 30° of amplitude. It is confirmed that the period changes less than 1% until the amplitude is 30°. On the other hand, the period increased by more than 10% when the amplitude became larger than 80°. At the end of his life he devised a scheme for using a pendulum to regulate a mechanical clock. However, the first reliable pendulum clock was only demonstrated by Huygens 15 years after Galileo's death.Q. How the time period of a pendulum was measured in the beginning of 16th century?

Attempt All sub parts from each question.Galileo’s Isochronous Pendulum: Galileo observed a lamp swinging from ceiling at Pisa cathedral ceiling. He was the first scientist to observe how long it took any object suspended from a rope or chain (a pendulum) to swing back and forth. There were no wrist watches at that time, so Galileo used his own pulse as a time measurement. Galileo observed that no matter how big the swings were, as in when the lamp was first swung, to how small the swings were as the lamp returned to a standstill, the time it took for each swing to complete was exactly the same. So, he concluded that the oscillations are isochronous. Anyhow, it was proved by advanced experimentation that the isochronism of simple pendulum is correct within 1% under the 30° of amplitude. It is confirmed that the period changes less than 1% until the amplitude is 30°. On the other hand, the period increased by more than 10% when the amplitude became larger than 80°. At the end of his life he devised a scheme for using a pendulum to regulate a mechanical clock. However, the first reliable pendulum clock was only demonstrated by Huygens 15 years after Galileo's death.Q. Who first observed the time period of a pendulum?

Attempt All sub parts from each question.Galileo’s Isochronous Pendulum: Galileo observed a lamp swinging from ceiling at Pisa cathedral ceiling. He was the first scientist to observe how long it took any object suspended from a rope or chain (a pendulum) to swing back and forth. There were no wrist watches at that time, so Galileo used his own pulse as a time measurement. Galileo observed that no matter how big the swings were, as in when the lamp was first swung, to how small the swings were as the lamp returned to a standstill, the time it took for each swing to complete was exactly the same. So, he concluded that the oscillations are isochronous. Anyhow, it was proved by advanced experimentation that the isochronism of simple pendulum is correct within 1% under the 30° of amplitude. It is confirmed that the period changes less than 1% until the amplitude is 30°. On the other hand, the period increased by more than 10% when the amplitude became larger than 80°. At the end of his life he devised a scheme for using a pendulum to regulate a mechanical clock. However, the first reliable pendulum clock was only demonstrated by Huygens 15 years after Galileo's death.Q. Galileo observed that the time period of the pendulum

Attempt All sub parts from each question.Galileo’s Isochronous Pendulum: Galileo observed a lamp swinging from ceiling at Pisa cathedral ceiling. He was the first scientist to observe how long it took any object suspended from a rope or chain (a pendulum) to swing back and forth. There were no wrist watches at that time, so Galileo used his own pulse as a time measurement. Galileo observed that no matter how big the swings were, as in when the lamp was first swung, to how small the swings were as the lamp returned to a standstill, the time it took for each swing to complete was exactly the same. So, he concluded that the oscillations are isochronous. Anyhow, it was proved by advanced experimentation that the isochronism of simple pendulum is correct within 1% under the 30° of amplitude. It is confirmed that the period changes less than 1% until the amplitude is 30°. On the other hand, the period increased by more than 10% when the amplitude became larger than 80°. At the end of his life he devised a scheme for using a pendulum to regulate a mechanical clock. However, the first reliable pendulum clock was only demonstrated by Huygens 15 years after Galileo's death.Q. Isochronism of simple pendulum is within acceptable limit as long as the amplitude is under

Attempt All sub parts from each question.Galileo’s Isochronous Pendulum: Galileo observed a lamp swinging from ceiling at Pisa cathedral ceiling. He was the first scientist to observe how long it took any object suspended from a rope or chain (a pendulum) to swing back and forth. There were no wrist watches at that time, so Galileo used his own pulse as a time measurement. Galileo observed that no matter how big the swings were, as in when the lamp was first swung, to how small the swings were as the lamp returned to a standstill, the time it took for each swing to complete was exactly the same. So, he concluded that the oscillations are isochronous. Anyhow, it was proved by advanced experimentation that the isochronism of simple pendulum is correct within 1% under the 30° of amplitude. It is confirmed that the period changes less than 1% until the amplitude is 30°. On the other hand, the period increased by more than 10% when the amplitude became larger than 80°. At the end of his life he devised a scheme for using a pendulum to regulate a mechanical clock. However, the first reliable pendulum clock was only demonstrated by Huygens 15 years after Galileo's death.Q. First reliable pendulum clock was only demonstrated by

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While noting the time period of a simple pendulum amplitude of vibration should be kept- A) reasonably large for easy measurements B)as small as possible C) reasonably constant D) very large as the value of t is very large?
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