Two identical point masses P and Q, suspended from two separate massless springs of spring constants k1 and k2, respectively, osc…

Question

Two identical point masses P and Q, suspended from two separate massless springs of spring constants k1 and k2, respectively, oscillate vertically. If their maximum speeds are the same, the ratio (AQ/AP) of the amplitude AQ of mass Q to the amplitude AP of mass P is:

1. A. k2/k1
2. B. k1/k2
3. C. k2/k1
4. D. k1/k2 (Correct answer)

Correct Answer

Option D — k1/k2

Detailed Solution & Explanation

The correct answer is $\sqrt{\dfrac{k_1}{k_2}}$.

Key Points

• Maximum speed $v_{max}=A\omega$, and it is equal for both: $A_P\omega_P=A_Q\omega_Q$.
• With $\omega=\sqrt{\dfrac{k}{m}}$ and equal masses: $\dfrac{A_Q}{A_P}=\dfrac{\omega_P}{\omega_Q}=\sqrt{\dfrac{k_P}{k_Q}}=\sqrt{\dfrac{k_1}{k_2}}$.