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 for a mass hanging on a spring is given by:

T = 2π√(m/k)

When the same mass is hung from a spring with a spring constant of 2k, the period of oscillation can be found by substituting 2k for k in the above equation:

T' = 2π√(m/2k) = (1/√2) * 2π√(m/k) = (1/√2) * T

Therefore, the period of oscillation decreases by a factor of approximately 1.41 or √2. The closest option is D, which states that the period decreases by a factor of approximately 1.41.

A Mass M Hanging on a Spring with a Spring