With a block of mass m, the frequency of a block-spring system is 1.5Hz. When 80g is added, the frequency drops to 0.9Hz. Find m and the spring constant k.
so w= 2pi*f
The Attempt at a Solution
The problem seems simple enough. I just have to set up 2 equations to solve one unknown and then find the other right?
So first i found the w for when the mass= m and f= 1.5Hz (i called this w) and the w for when mass= m+0.08 and f= 0.9Hz (W).
Using the formula w= 2pi*f, i found 9.42 for w and 5.65 for W.
Then I set up the 2 equations:
k = mw^2 = 88.8m
k = (m+0.08)W^2 = 31.9m + 2.55
After i did equation 1 = equation 2, so:
88.8m = 31.9m + 2.55 and this gave me m=22.3
But the correct answer for m is supposed to be 0.045 kg. Can somebody let me know what I'm doing wrong please?
The correct value for k is supposed to be 3.99N/m