Vision is blurred if the head is vibrated at 29 Hz because the vibrations are resonant with the natural frequency of the eyeball
1 answer:
The effective spring constant of the system is 39.6 N/m
Explanation:
The frequency of oscillation of a spring-mass system is given by
where
k is the spring constant of the system
m is the mass
In this problem, we have:
f = 29 Hz is the frequency of vibration of the eyeball system
m = 7.5 g = 0.0075 kg is the mass
We can therefore re-arrange the equation to find the effective spring constant of the system. We find:
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Here is the link to the spreadsheet:
https://docs.google.com/spreadsheets/d/1SkQHbI1BxiJnwpWbLmP0XWgcNPrGquH1K2MfN6cznVo/edit?usp=sharing
Center of mass is the point such that if you apply force to it, the system would move without rotating.
We can use following formula to calculate the center of mass:
Where M is the sum of the masses of all particles.
Part 1
To calculate the x coordinate of the center of mass we will use this formula:
I will do all the calculations in the google sheet that I will share with you.
For the x coordinate of the center of mass we get:
Part 2
To calculate the y coordinate of the center of mass we will use this formula:
I will do all the calculations in the google sheet that I will share with you.
For the x coordinate of the center of mass we get:
Part 3
We will calculate speed along x and y-axis separately and then will add them together.
Total velocity is:
Once we calculate velocities we get:
Part 4
Because origin is left to our center of mass(please see the attached picture) placing fifth mass in the origin would move the center of mass to the left along the x-axis.
Part 5
If you place fifth mass in the center of the mass nothing would change. The center of mass would stay in the same place.
Here is the link to the spreadsheet:
https://docs.google.com/spreadsheets/d/1SkQHbI1BxiJnwpWbLmP0XWgcNPrGquH1K2MfN6cznVo/edit?usp=sharing