The mass 'm' oscillates in simple harmonic motion with an amplitude 'A' as shown in the figure.
The amplitude of point \(P\) is
The mass 'm' oscillates in simple harmonic motion with an amplitude 'A' as shown in the figure.
The amplitude of point \(P\) is
Show Hint
- \( \frac{K_1 A}{K_2} \)
- \( \frac{K_2 A}{K_1} \)
- \( \frac{K_1 A}{K_1 + K_2} \)
- \( \frac{K_2 A}{K_1 + K_2} \)
The Correct Option is D
Solution and Explanation
In a system with two springs \(K_1\) and \(K_2\) connected in series, the effective spring constant \(K_{{eff}}\) is given by: \[ \frac{1}{K_{{eff}}} = \frac{1}{K_1} + \frac{1}{K_2} \] \[ K_{{eff}} = \frac{K_1 K_2}{K_1 + K_2} \] The amplitude of point \(P\) is determined by the ratio of the spring constants.
The displacement of point \(P\) relative to the mass \(m\) is: \[ A_P = \frac{K_2}{K_1 + K_2} A \] Final Answer: \( \frac{K_2 A}{K_1 + K_2} \)
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