A mass-spring oscillating system undergoes SHM with maximum amplitude A. If the spring constant is doubled what effect will it produce on the mechanical energy of the system
Question
A mass-spring oscillating system undergoes SHM with maximum amplitude A. If the spring constant is doubled what effect will it produce on the mechanical energy of the system
Solution
The mechanical energy of a mass-spring system undergoing Simple Harmonic Motion (SHM) is given by the formula:
E = 1/2 k A^2
where: E is the mechanical energy, k is the spring constant, and A is the amplitude of the motion.
If the spring constant k is doubled, the new mechanical energy E' of the system will be:
E' = 1/2 * 2k * A^2 = k * A^2
So, the mechanical energy of the system will also be doubled. This is because the mechanical energy of the system is directly proportional to the spring constant. Therefore, if the spring constant is doubled, the mechanical energy of the system will also double, assuming the amplitude remains constant.
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