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)
Answer:
$16
Step-by-step explanation:
You would just multuply the amount of time and the amount of money it costs.
Answer:
20, 000
Step-by-step explanation:
For a duration of 50 years, the consumption will be equal to the product of annual consumption and the number of years hence 800*50=40, 000 barrels.
Since 20, 000 barrels are unknown and they are part if consumption in the next 50 years, then the known or proven reserves will be given by getting the difference between total consumption and unknown reserve, expressed as 40, 000-20, 000=20, 000 barrels.
Answer:
p=-7 :)
Step-by-step explanation:
-13-8=3p
-13+(-8)=3p
-21=3p
÷3
-7=p
