A spring of force constant is cut into lengths of ratio . They are connected in series and the new force constant is . They are connected in parallel and the force constant is . Then is:
Step1: Given data
Step2: Spring constant
Step4: Finding the spring constants
Let L be the length of the spring and it is cut into three segments of ratio . So, the three segments are , , .
As we know .So, the spring constant of the spring segments are
So, the spring constant of the spring system when they are connected in series is
Again, the spring constant of the spring system when connected parallel is
Step5: Finding the ratio
Now, the ratio of the two given spring systems is
Therefore, the ratio of spring constant is .