Answer:
x = -5 sin (2t)
Step-by-step explanation:
k is the spring stiffness. The unstretched length of the spring is L.
When the mass is added, the spring stretches to an equilibrium position of L+s, where mg = ks. When the mass is displaced a distance x (where x is positive if the displacement is down and negative if it's up), the spring is stretched a total distance s + x.
There are two forces on the mass: weight and force from the spring. Sum of the forces in the downward direction:
∑F = ma
mg − k(s + x) = ma
mg − ks − kx = ma
Since mg = ks:
-kx = ma
Acceleration is second derivative of position, so:
-kx = m d²x/dt²
Let's find k:
F = kx
400 = 2k
k = 200
We know that m = 50. Substituting:
-200x = 50 d²x/dt²
-4x = d²x/dt²
d²x/dt² + 4x = 0
This is a linear second order differential equation of the form:
x" + ω² x = 0
The solution to this is:
x = A cos (ωt) + B sin (ωt)
Here, ω² = 4, so ω = 2.
x = A cos (2t) + B sin (2t)
We're given initial conditions that x(0) = 0 and x'(0) = -10 (remember that down is positive and up is negative).
Finding x'(t):
x' = -2A sin (2t) + 2B cos (2t)
Plugging in the initial conditions:
0 = A
-10 = 2B
Therefore:
x = -5 sin (2t)
Applying BODMAS (Order of operations rule)
Where: B is for brackets
O is for 'of' which means multiplication
D is for division
M is for multiplication
A is for addition
S is for subtraction
<u>In this case:</u>
We start with addition then we go to addition and finally we subtract.
(78 × 13) - (8 × 78) + (26 × 78) - 78
= 1014 - 624 + 2028 - 78
= 1014 + 2028 - 624 - 78
= 3042 - 624 - 78
=2340
Answer:
2-----10
1-----5
3-----15
Step-by-step explanation:
For every 1 cup of blue paint, there are 5 cups of yellow paint
Hope this helps!
<span>Simplifying
2x + -1y = 9
Solving
2x + -1y = 9
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add 'y' to each side of the equation.
2x + -1y + y = 9 + y
Combine like terms: -1y + y = 0
2x + 0 = 9 + y
2x = 9 + y
Divide each side by '2'.
x = 4.5 + 0.5y
Simplifying
x = 4.5 + 0.5y
Hope this helps :)
~I tried to space it out so it wont look like a bunch of mess scrambled up xD~</span>
If you want the expression, the expression would be:
3.5x+50
