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:
Positive velocity and negative acceleration
Explanation:
An object moving in the positive direction has a positive velocity.
An object that's slowing down while moving in the positive direction has a negative acceleration.
Answer:
When light is scattered, It reflects in many different directions, think about sunlight reflecting off the clouds.
Physical changes do not change the identity of the substance. Heat causes chemical reactions. You cannot see chemical changes with the naked eye. The identity of a substance changes like when you burn paper, from paper it turns into ash and produces smoke, which are products from the chemical reactions.
Answer:
50 degrees
Explanation:
Usually in physics in solving such questions refractive index of air is taken as 1.00 (n=1.00) by assuming that air is a vacuum. Hence, the light ray passes from water to air at an angle of incident of 40 degrees, it means that it has angle of 50 degrees to the normal line.