TS EAMCET · Physics · Oscillations
A particle is executing simple harmonic motion. If the force acting on the particle at a position is \(86.6 \%\) of the maximum force on it, then the ratio of its velocity at that point and its maximum velocity is
- A \(1: \sqrt{3}\)
- B \(1: 2\)
- C \(\sqrt{3}: 2\)
- D \(1: 3\)
Answer & Solution
Correct Answer
(B) \(1: 2\)
Step-by-step Solution
Detailed explanation
\(F = 0.866 F_{max} \Rightarrow kx = 0.866 kA \Rightarrow x = 0.866 A\) \(v = \omega \sqrt{A^2 - x^2} = \omega \sqrt{A^2 - (0.866 A)^2} = \omega A \sqrt{1 - 0.866^2}\) \(v = \omega A \sqrt{1 - 0.75} = \omega A \sqrt{0.25} = 0.5 \omega A\) \(v_{max} = \omega A\)…
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