Answer:
The frequency as calculated is 0.79 Hz
Solution:
As per the question:
Mass of the beam, m = 225 kg
Mass of the sack, m' = 175 kg
Amplitude, A = 40.0 cm = 0.4 m
Frequency, f = 0.6 Hz
Now,
(A) To calculate the frequency of the SHM:
The total mass, M = m + m' = 225 + 175 = 400 kg
With the help of the eqn:
[tex]f = \frac{1}{2\pi}\sqrt{\frac{k}{M}}[/tex]
where
k = spring constant
Thus
[tex]0.6 = \frac{1}{2\pi}\sqrt{\frac{k}{400}}[/tex]
[tex]0.6\times 2\pi \times 20 = \sqrt{k}[/tex]
Squaring both sides, we get:
k = 5684.89 N/m
Now, after the gravel has fallen:
m = 275 kg
Now,
The frequency of the SHM can be calculated as:
[tex]f_{s} = \frac{1}{2\pi}\sqrt{\frac{5684.89}{225}}[/tex]
[tex]f_{s} = 0.79\ Hz[/tex]
