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A particle performs simple harmonic motion under a force F1, and its period is 4/5 s. When the force is replaced by F2, the period becomes 3/5 s. If F1 and F2 act together on the particle in the same direction, what is the resulting period of oscillation in seconds?
- 12/25
- 7/5
- 24/25
- 5/7
Correct answer: 12/25
Solution
k ~ 1/T^2, and combining forces adds the constants: 1/T^2 = 1/T1^2 + 1/T2^2 = (5/4)^2 + (5/3)^2 = 25/16 + 25/9. This gives T^2 = 144/625, so T = 12/25 s.
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