Practice question for mass-spring systems

1. Learning Object 1 Lyndon Won
Spring Systems
Question: There are 2 horizontal mass-spring systems (shown below). The mass of A is twice
that of B. The spring constant of B is 3 times that of A. The rest lengths are equal. How does the
period of A compare that of B (how many times larger is one compared to the other)?
Diagram A
Diagram B

2. Learning Object 1 Lyndon Won
Spring Systems
Solution:
The equation for period is T = 2π sqrt(m/k)
First, plug in the values for A:
T = 2π sqrt(2m/k)
Next, input values for B:
T = 2π sqrt(m/3k)
Since both use the variables m and k, they can be ignored
Therefore the equation for A can be simplified to:
T = 2π sqrt(2/1) = 2π sqrt(2)
And B:
T = 2π sqrt(1/3)
Then to find how many times larger A is then B:
2π sqrt(2) = sqrt(2) = 2.45
2π sqrt(1/3) sqrt(1/3)
Therefore the period of A is 2.45 times longer than the period of B