By what factor must one change the weight suspended vertically from a spring coil in order to increase its period of simple harmonic motion by five?
A)1/25
B)1/5
C)5
D)25
E)1

Question

Quizplus · Accepted Answer

The period of simple harmonic motion of a spring is given by T = 2π√(m/k), where m is the mass attached to the spring and k is the spring constant. If we want to increase the period by a factor of 5, we need to have T' = 5T. Substituting T in the equation above, we get:

5T = 2π√(m'/k)

Squaring both sides, we get:

25T^2 = 4π^2(m'/k)

Dividing the second equation by the first, we get:

25 = (m'/m)

So to increase the period by a factor of 5, we need to increase the mass by a factor of 25. Therefore, the weight suspended vertically from the spring coil must be increased by a factor of 25, or D.

By What Factor Must One Change the Weight Suspended Vertically