Answer:
The function is x = e^(-t/2) * (0.792*sin12t + 5cos12t)
Explanation:
we have to:
m = mass = 4 kg
k = spring constant = 577 N/m
c = damping constant = 4 N*s/m
The differential equation of motion is equal to:
m(d^2x/dt^2) + c(dx/dt) + k*x = 0
Replacing values:
4(d^2x/dt^2) + 4(dx/dt) + 577*x = 0
Thus, we have:
4*x^2 + 4*x + 577 = 0
we will use the quadratic equation to solve the expression:
x = (-4 ± (4^2 - (4*4*577))^1/2)/(2*4) = (-4 ± (-9216))/8 = (1/2) ± 12i
The solution is equal to:
x = e^(1/2) * (c1*sin12t + c2*cos12t)
x´ = (-1/2)*e^(1/2) * (c1*sin12t + c2*cos12t) + e^(-t/2) * (12*c1*cos12t - 12*c2*sin12t)
We have the follow:
x(0) = 5
e^0(0*c1 + c2) = 5
c2 = 5
x´(0) = 7
(-1/2)*e^0 * (0*c1 + c2) + e^0 * (12*c1 - 0*c2) = 7
(-1/2)*(5) + 12*c1 = 7
Clearing c1:
c1 = 0.792
The function is equal to:
x = e^(-t/2) * (0.792*sin12t + 5cos12t)
Explanation:
Watts are defined as 1 Watt = 1 Joule per second (1W = 1 J/s)
which means that 1 kW = 1000 J/s. A Watt is the amount of energy (in Joules) that an electrical device (such as a light) is burning per second that it's running.
The disposition of the toxic waste materials is the greatest problem
in the field of nuclear-generated electric power today.
Nuclear-generated electric power generates NO air pollution, and
we have the mature technology to use it widely.
Answer:
3.5 N
Explanation:
Let the 0-cm end be the moment point. We know that for the system to be balanced, the total moment about this point must be 0. Let's calculate the moment at each point, in order from 0 to 100cm
- Tension of the string attached at the 0cm end is 0 as moment arm is 0
- 2 N weight suspended from the 10 cm position: 2*10 = 20 Ncm clockwise
- 2 N weight suspended from the 50 cm position: 2*50 = 100 Ncm clockwise
- 1 N stick weight at its center of mass, which is 50 cm position, since the stick is uniform: 1*50 = 50 Ncm clockwise
- 3 N weight suspended from the 60 cm position: 3*60 = 180 Ncm clockwise
- Tension T (N) of the string attached at the 100-cm end: T*100 = 100T Ncm counter-clockwise.
Total Clockwise moment = 20 + 100 + 50 + 180 = 350Ncm
Total counter-clockwise moment = 100T
For this to balance, 100 T = 350
so T = 350 / 100 = 3.5 N