Answer:
6 rad/s
Explanation:
In a spring the angular frequency is calculated as follows:
where 
is the angular frequency, 
is the mass of the object in this case 
, and 
is the constant of the spring.
To calculate the angular frequency, first we need to find the constant which is calculated as follows:
Where 
is the force: 
, and 
is the distance from the equilibrium position: 
.
Thus the spring constant:
And now we do have everything necessary to calculate the angular frequency:
the angular frequency of the oscillation is 6 rad/s
Answer:
A negative slope results when an individual is moving away
Explanation:
Answer: 0.53m
Explanation:
According to the equation of motion v²= v₀²+2as
Since the body is launched upward, the final velocity at the maximum height will be "zero" since the body will momentarily be at rest at the maximum height i.e v = 0
Initial velocity given (v₀) = 3.25 m/s
The body is also under the influence of gravity but the acceleration due to gravity will be negative being an upward force (a = -g) and the distance (s) will serve as our maximum height (h)
The equation of motion will.now become
V = v₀² -2gh
Where v = 0 v₀ = 3.25m/s g = 10m/s h = ?
0 = 3.25² - 2(10)h
0 = 10.56 - 20h
-10.56 = -20h
h = 10.56/20
h = 0.53m
Therefore, the maximum height, h (in meters), above the launch point that the basketball will achieve is 0.53m
This bifurcation is called a saddle-node bifurcation. In it, a pair of hyperbolic equilibria, one stable and one unstable, coalesce at the bifurcation point, annihilate each other and disappear.
<h3>What is a bifurcation equilibria?</h3>
- The mathematical study of changes in a family of curves' qualitative or topological structure, such as the integral curves of a family of vector fields or the solutions to a family of differential equations, is known as bifurcation theory.
- A bifurcation happens when a tiny, gradual change in a system's parameter values (the bifurcation parameters) results in an abrupt, "qualitative," or topological change in the system's behavior.
- This term is most frequently used to refer to the mathematical study of dynamical systems.
- Both continuous systems (represented by ordinary, delay, or partial differential equations) and discrete systems can experience bifurcations (described by maps).
To learn more about bifurcation equilibria, refer to
brainly.com/question/14728055
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