Question

The mass 'm' oscillates in simple harmonic motion with an amplitude 'A' as shown in the figure. 
The amplitude of point \(P\) is 

 

 

• A. \( \frac{K_1 A}{K_2} \)
• B. \( \frac{K_2 A}{K_1} \)
• C. \( \frac{K_1 A}{K_1 + K_2} \)
• D. \( \frac{K_2 A}{K_1 + K_2} \)

Hint:

In systems with multiple springs, the effective spring constant and the distribution of amplitudes depend on the configuration of the springs (series or parallel).

Answer 1

The Correct Option is D

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:  \( \frac{K_2 A}{K_1 + K_2} \)