A simple pendulum of length l has total energy E at amplitude A. If its length is doubled while keeping amplitude constant, what is the new energy___________________?
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Answer: B. E/2
Explanation
Pendulum energy is proportional to length when amplitude angle remains constant. Doubling the pendulum length doubles the potential energy scale proportionally. Linear amplitude constraints result in the energy halving relative to the system changes. A simple pendulum consists of a point mass suspended by a light inextensible string. Total energy in simple harmonic motion depends on mass, gravitational acceleration, and length. Potential energy reaches its maximum value at the extreme displacement amplitudes of swing.
Clock makers and physicists study pendulum mechanics to build accurate timekeeping devices. Conservation of energy governs the continuous interchange between kinetic and potential energy. Understanding pendulum behavior helps explain harmonic oscillations in mechanical engineering. Stating energy remains equal ignores the direct proportionality between length and total energy. Doubling the energy misinterprets how linear amplitude constraints interact with length changes. Four times the energy incorrectly applies a squared relationship rather than linear scaling.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
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