By what factor must one change the weight suspended vertically from a spring coil in order to triple its period of simple harmonic motion?
A)1/9
B)0.33
C)3.0
D)9.0

Question

Quizplus · Accepted Answer

The period of simple harmonic motion of a spring-mass system is given by T=2π√(m/k), where m is the mass suspended from the spring and k is the spring constant. If we want to triple the period, we need to increase T by a factor of 3. Using the equation T=2π√(m/k), we can see that T is proportional to the square root of m/k. Therefore, we need to increase m/k by a factor of 9 in order to triple the period. Since k is a constant for a given spring, we need to increase the mass by a factor of 9. Hence, the weight suspended vertically from the spring coil must be increased by a factor of 9. Therefore, the correct answer is D.

By What Factor Must One Change the Weight Suspended Vertically