Abrick of mass 8 kg hangs from the end of a spring. when the brick is at rest, the spring is stretched by 3 cm. the spring is then stretched an additional 4 cm and released. assume there is no air resistance. note that the acceleration due to gravity, g, is g=980 cm/s2. set up a differential equation with initial conditions describing the motion and solve it for the displacement s(t) of the mass from its equilibrium position (with the spring stretched 3 cm). s(t)= 4 cos(sqrt(980/3)t) cm

s(t) = 0.04cos(sqrt(980/3))

Step-by-step explanation:

Find spring constant. Use balance force between weight of brick and spring elastic force when brick at rest:

Weight of brick = force of spring

mg = kx

Mass brick, m = 8kg

Gravity constant, g = 9.8 m/s2

Spring elongation,x = 0.03m

Hence, spring constant, k= mg/x

= 8*9.8/0.03

= 7840/3

Since there is no other external forces, spring acts in simple harmonic motion

-kx = ma

a = -kx/m

note that a is the acceleration which is the double derivative of distance over time. Hence

d2y/dx2 = -kx/m

d2y/dx2 + kx/m = 0

Note that this equation is similar to simple harmonic motion:

d2y/dx2 + (w2)x = 0

Comparing these two equations we found:

w2 = k/m

Using the values obtained earlier:

w2 = (7840/3)/8 = 980/3

w = sqrt(980/3) = 18.07 rad/s

Since the movement of the spring will be sinusoidal, similar to the movement of pendulum, we use the general equation for oscillating motion:

s(t) = A sin (wt + c)

Note that in initial condition when t=0,

displacement of spring s = A = 0.04m

Hence 0.04 = 0.04 sin(0+c)

sin c = 1

c = π/2 - hence indicating that the motion is π/2 further than the equation.

Using trigonometry identity, we know that cos(theta) = sin(π/2 + theta)

So, we can change sin(wt+π/2) to cos(wt)

Updating the equation, we'll get

s(t) = 0.04 cos(wt).

w = sqrt(980/3)

Finally,

s(t) = 0.04cos(sqrt(980/3)) (in m)

Or

s(t) = 4cos(sqrt(980/3)) (in cm)

median is the value separating the higher half of a data sample, a population or probablity distribution from the lower half.

step-by-step explanation:

say you have 3,8,7,3,1,9,8 order them from lowest to highest

if orderd it would be 1,3,3,7,8,8,9 now you take away from the lowest and the highest until you end up in the middle.

so you would remove the 1 and 9 leaving you with 5 digits remaining

when you've reached the middle that would be your answer so in this case the answer is 7

if there were two numbers left say 7 and 5 you'd and them together so 12 then divide by 2 witch would equal 6 so the answer would be 6

good luck on that project hoped i you at all

2.2°  

step-by-step explanation:

let θ = the angle of elevation.

tanθ =77/2020

tanθ = 0.038 12

      θ = tan⁻¹0.038 12

      θ = 2.2°