If the maximum displacement of a spring is doubled, calculate the change in thefollowing parametersi) Periodic time ii) maximum velocity iii) maximum acceleration
Question
If the maximum displacement of a spring is doubled, calculate the change in thefollowing parametersi) Periodic time ii) maximum velocity iii) maximum acceleration
Solution
The parameters you mentioned are governed by the following formulas in simple harmonic motion:
i) Periodic time (T) = 2π√(m/k), where m is the mass and k is the spring constant. The periodic time is independent of the amplitude (maximum displacement). Therefore, if the maximum displacement of the spring is doubled, the periodic time will remain the same.
ii) Maximum velocity (v_max) = ωA, where ω is the angular frequency and A is the amplitude. If the amplitude is doubled, the maximum velocity will also be doubled.
iii) Maximum acceleration (a_max) = ω²A, where ω is the angular frequency and A is the amplitude. If the amplitude is doubled, the maximum acceleration will also be doubled.
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