(i) One month later, the tower is holding 21.5 million kilograms of water, when it experiences a gust of wind that again gives it a speed of 0.24 m/s. What function will describe the displacement of the tower? (j) Make a plot of the position function from (i). (k) What is the period of the new oscillation? You can use your graph as an aid, but use your function from to get the exact value.
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
![NEED PARTS I-M PLEASE
A large water tower holds 3 million gallons of water, which has a mass of about 11 million kilograms.
When the wind blows, this causes the steel structure to sway back and forth due to the force. An
engineer studying the tower observes that a steady wind at a speed of 35 mph exerts a force of 1.45
million Newtons on the tower, causing it to lean 0.27 meters away from equilibrium. The engineer
begins by assuming that the restoring force is proportional to the displacement F = -kx, so that
the motion of the system can be modeled by the differential equation mx" + kx = 0. Here m is the
mass of the tower, k is the spring constant, and x is the displacement of the tower away from its
equilibrium position.
(a) What is the spring constant k of the steel structure? Be sure to use the right units!
(b) Write the general solution to the differential equation.
(c) What is the angular frequency w at which the tower oscillates?
(d) Suppose that the tower is sitting comfortably in equilibrium when a sudden brief gust of wind
gives the to
of the tower changes after this?
a velocity of 0.24 meters per second. What function will describe how the position
(e) Make a plot of the position function from (d).
(f) What is the maximum displacement away from equilibrium that the water tower goes? You can
use your graph as an aid, but use your function from (d) to get the exact value.
(g) What is the period of the oscillation? That is, how much time does it take the tower to go
through one complete cycle?
(h) How would your plot be different if there had been a stronger gust of wind? What would be the
same? What would be different?
(i) One month later, the tower is holding 21.5 million kilograms of water, when it experiences a gust
of wind that again gives it a speed of 0.24 m/s. What function will describe the displacement of
the tower?
(j) Make a plot of the position function from (i).
(k) What is the period of the new oscillation? You can use your graph as an aid, but use your
function from to get the exact value.
(1) The steel framework will experience a catastrophic structural failure if it sways more than 1.2
meters. What is the maximum speed that a gust of wind can give the tower while it's holding
21.5 million kg of water before this causes unpleasant results.
(m) Another engineer studies a similar tower in the neighboring town, finding that while this contains
on 9.5 million kilograms of water, it tends to sway back and forth with an angular frequency of
approximately 0.55 rad/s. What must be the spring constant of the structure holding up this
water tower?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a8e0411-af3c-4fe9-9f60-29bf0a08ded5%2Fbee1edde-0838-4347-91bd-233fbdeeae3d%2Ff6z2mxl_processed.jpeg&w=3840&q=75)
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