By what factor must one change the weight suspended vertically from a spring coil in order to double its period of simple harmonic motion?
A) 4
B) 2
C) 1/2
D) 1/4

Question

Quizplus · Accepted Answer

The period of simple harmonic motion is given by:
T = 2π√(m/k)
Where T is the period, m is the mass of the suspended weight, and k is the spring constant.
To double the period, we need to make T=2T. Therefore:
2T = 2π√(m/k)
T = π√(m/k)
(2π√(m/k)) / (π√(m/k)) = √(m/k) / √(m/k/4) = 2
Therefore, we need to change the weight suspended by a factor of 2^2 = 4 to double its period of simple harmonic motion.

By What Factor Must One Change the Weight Suspended Vertically