Question

A mass on a spring A oscillates at twice the frequency of the same mass on spring B. Which statement is correct?A.The spring constant for B is one quarter of the spring constant for A.B.The spring constant for B is 4 times the spring constant for A.C.The spring constant for B is half of the spring constant for A.D.The spring constant for B is 1.41 times the spring constant for A.E.The spring constant for B is twice the spring constant for A.

Answer 1

Answer:

A.The spring constant for B is one quarter of the spring constant for A.

Explanation:

If spring A oscillates at twice the frequency of spring B, and period is frequency inverted. It means spring B has a period twice of spring A's.

$T_B = 2T_A$

As $T = 2\pi\sqrt{\frac{m}{k}}$, and the 2 springs have the same mass

$2\pi\sqrt{\frac{m}{k_B}} = 2\pi\sqrt{\frac{m}{k_A}}$

$\sqrt{k_A} = 2\sqrt{B}$

$k_A = 4k_B$

$k_B = k_A/4$

So A.The spring constant for B is one quarter of the spring constant for A. is the correct answer.