# SHM mass and spring constant with given frequency

k77i

## Homework Statement

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.

T=1/f
w=2pi/T
so w= 2pi*f
w^2=k/m
so k=mw^2
T=2pi*sqrt(m/k)

## 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
and
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

Homework Helper
Gold Member
88.8m = 31.9m + 2.55 and this gave me m=22.3

Try redoing the above step again. I think that's where the trouble is coming from.

k77i
I'm not exactly sure which steps you're asking me to redo but i'll show my calculations in more detail if that's what you meant.

w= 2pi*f1 = 2pi*1.5 = 9.42 rad/s
W= 2pi*f2 = 2pi*0.9 = 5.65 rad/s

Then,

1) k= mw^2 = m*9.42^2 = 88.8m
2) k= W^2(m+0.08) = 5.65^2(m+0.08) = 31.9m + 2.55

I really still don't see what's wrong with the way I'm doing it..

Homework Helper
Gold Member
I'm not exactly sure which steps you're asking me to redo but i'll show my calculations in more detail if that's what you meant.

w= 2pi*f1 = 2pi*1.5 = 9.42 rad/s
W= 2pi*f2 = 2pi*0.9 = 5.65 rad/s

Then,

1) k= mw^2 = m*9.42^2 = 88.8m
2) k= W^2(m+0.08) = 5.65^2(m+0.08) = 31.9m + 2.55

I really still don't see what's wrong with the way I'm doing it..

So far so good. It's the next step where you solve for m (after you set the equations equal).

k77i
Well ok..

Equation 1 = Equation 2

88.8m = 31.9m + 2.55

then bring the "m" terms to one side

88.8m - 31.9m = 2.55

56.6m = 2.55

and then divide..

Ahhh!! wow i feel really stupid.. i was dividing both sides by 2.55 all this time.. I get it now, thanks a lot