Which of the following massspring systems will have the high

Which of the following mass-spring systems will have the highest frequency of vibration?

Case A: A spring with a k=300 N/m and a mass of 200 g suspended from it.

or

Case B: A spring with a k=400 N/m and a mass of 200 g suspended from it.

Which of the following mass-spring systems will have the highest frequency of vibration?

Case A: A spring with a k=300 N/m and a mass of 200 g suspended from it.

or

Case B: A spring with a k=300 N/m and a mass of 100 g suspended from it.

Solution

for Spring -mass SHM:

m w^2 = k

w = sqrt(k/m)

set which highest sqrt(k/m) will have highest frquency.

A: sqrt(300/0.200) = 38.7 rad/s

B: sqrt(400/0.200) = 44.7 rad/s

hence Ans(B)