Given the following data:
Initial frequency = 0.83 Hz.
Additional mass = 780 grams to kg = 0.78 kg
New frequency = 0.60 Hz
To determine the value of the initial mass, m, we would apply the following formula:
;f=1/2л⟌k/m
Where:
F is the frequency.
m is the mass
k is the spring constant.
For mass (m):
0.83=1/2л⟌k/m ...equation 1.
For additional mass:
0.60=1/2⟌k/m+0.78 ...equation 2.
Next, we would divide eqn. 1 by eqn. 2:
;0.83/0.60=1/2л⟌((k/m)/1)/2л⟌m+0.78
1.3833=⟌k/m/⟌k/m+0.78
Taking the square of both sides, we have:
1.9135=k/m/k/m+0.78
1.9135=k/m×m+0.78/k
1.9135=m+0.78/m
1.9135m-m=0.78
0.9135m=0.78
m=0.78/0.9135
m=0.8538kg
the value of mass is 0.8538.
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