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)
Answer:
14.85 m/s
Explanation:
From the question given above, the following data were obtained:
Height (h) of tower = 45 m
Horizontal distance (s) moved by the balloon = 45 m
Horizontal velocity (u) =?
Next, we shall determine the time taken for the balloon to hit the shoe of the passerby. This is illustrated below:
Height (h) of tower = 45 m
Acceleration due to gravity (g) = 9.8 m/s²
Time (t) =?
h = ½gt²
45 = ½ × 9.8 × t²
45 = 4.8 × t²
Divide both side by 4.9
t² = 45/4.9
Take the square root of both side
t = √(45/4.9)
t = 3.03 s
Finally, we shall determine the magnitude of the horizontal velocity of the balloon as shown below:
Horizontal distance (s) moved by the balloon = 45 m
Time (t) = 3.03 s
Horizontal velocity (u) =?
s = ut
45 = u × 3.03
Divide both side by 3.03
u = 45/3.03
u = 14.85 m/s
Thus, the magnitude of the horizontal velocity of the balloon was 14.85 m/s
Answer:
1 km = 1000 m
1 m = 100 cm
1 m = 1000 mm
1 cm = 10 mm
hope this helps u figure it out :)
Answer:
The magnetic force can act from a distance because of the magnetic field that is created around it. It can be defined as imaginary lines around the magnet upto which it has magnetic force.
If a piece of iron is put into the magnetic field but has a slight distance from the magnet, it will be pulled towards the magnet because it is in its magnetic field.
The south pole and the north poles of the magnet has effect on each other. Same poles repeal each other and opposite poles attract each other resulting in forming a field of attraction or repulsion.
The imaginary lines created are known as magnetic field which is responsible for the magnetic force from a distance.
In a circuit, if the resistors were decreased by a factor of 1,000, it is true that the current would increase by a factor of 1,000, according to Ohm's Law.
<h3>What is Ohm's Law?</h3><h3 />
It is a law in electricity that posits that the voltage that goes through a conductor is directly proportional to the current.
<h3>How does Ohm'slaw explain the change in current?</h3>
One formula in Ohm's law is:
Voltage = Current x Resistance
If the resistance were to decrease by a factor of 1,000, the current would have to increase by a factor of 1,000 as well in order to give the same voltage.
Find out more on Ohm's law at brainly.com/question/14296509.