A mass m hanging on a spring with a spring constant k executes simple harmonic motion with a period T. If the same mass is hung from a spring with a spring constant of 2k, the period of oscillation
A) increases by a factor of 2.
B) decreases by a factor of 2.
C) increases by a factor of .
D) decreases by a factor of .
E) is not affected.

Question

A mass m hanging on a spring with a spring constant k executes simple harmonic motion with a period T. If the same mass is hung from a spring with a spring constant of 2k, the period of oscillation
A) increases by a factor of 2. 
B) decreases by a factor of 2. 
C) increases by a factor of . 
D) decreases by a factor of . 
E) is not affected.

Quizplus · Accepted Answer

The period of simple harmonic motion is given by T=2π√(m/k), where m is the mass and k is the spring constant. Thus, when the mass is hung from a spring with spring constant 2k, the period becomes T=2π√(m/(2k))=π√(m/k). This is a factor of √2 smaller than the original period, so the period decreases by a factor of √2, which is approximately 1.41 or 11eaa4be_8521_d5fd_9e4a_1712379399fc_TB6080_11. Therefore, the correct choice is D.

A Mass M Hanging on a Spring with a Spring