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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.

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MechEngineer

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.

[tex]T_B = 2T_A[/tex]

As [tex] T = 2\pi\sqrt{\frac{m}{k}}[/tex], and the 2 springs have the same mass

[tex]2\pi\sqrt{\frac{m}{k_B}} = 2\pi\sqrt{\frac{m}{k_A}}[/tex]

[tex]\sqrt{k_A} = 2\sqrt{B}[/tex]

[tex]k_A = 4k_B[/tex]

[tex]k_B = k_A/4[/tex]

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

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