Question
In: Advanced Math
Suppose a water tower in an earthquake acts as a mass-spring system. Assume that the container...
Suppose a water tower in an earthquake acts as a mass-spring system. Assume that the container on top is full and the water does not move around. The container then acts as a mass and the support as a spring, where the induced vibrations are horizontal. Suppose that the container with water has a mass of m = 10, 000 kg. It takes a force of 1000 Newtons to displace the container 1 m. For simplicity assume no friction. When the earthquake hits, the water tower is at rest (not moving). Suppose the earthquake induces an external force F(t) = A cos(ωt)
Find the solution to the Initial Value Problem
Solutions
Colby Messinger answered 1 year agoRelated Solutions
A fixed-mass system contains water (H20) in a rigid (fixed-volume) container. The mass of the water...
A fixed-mass system contains water (H20) in a rigid
(fixed-volume) container. The mass of the water is mass, m=
1.805719781 kgs. A process occurs having the following initial and
final thermodynamic properties.
Initial Pressure: P1 = 1000kPa Initial Temperature:
T1 = 600 oC Final Temperature: T2 = 140
oC
Determine the following: (Neglect changes in kinetic and
potential energy)
1. 1W2 (work done on.by the system, in kJoules)
2. 1Q2 (heat transfer to/from the system, in
kJoules)
3. (S2 - S1)sys...
Suppose that the mass in a mass-spring-dashpot system with m = 10, the damping constant c...
Suppose that the mass in a mass-spring-dashpot system with m =
10, the damping constant c = 9, and the spring constant k = 2 is
set in motion with x(0) = -1/2 and x'(0) = -1/4.
(a) Find the position function x(t).
(b) Determine whether the mass passes through its equilibrium
position. Sketch the graph of x(t).
If an undamped spring-mass system with a mass that weighs 24 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 24 lb
and a spring constant 9 lbin is suddenly set in motion at t=0 by an
external force of 180cos(8t) lb, determine the position of the mass
at any time. Assume that g=32 fts2. Solve for u in feet.
If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 6 lb
and a spring constant 9 lb/in is suddenly set in motion at t=0 by
an external force of 99cos(20t) lb, determine the position of the
mass at any time. Assume that g=32 ft/s2. Solve for u in feet.
If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 6 lb
and a spring constant 9 lbin is suddenly set in motion at t=0 by an
external force of 33cos(20t) lb, determine the position of the mass
at any time. Assume that g=32 fts2. Solve for u in feet.
Enclose arguments of functions in parentheses. For example,
sin(2x).
u(t)=?
If an undamped spring-mass system with a mass that weighs 24 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 24 lb
and a spring constant 9 lbin is suddenly set in motion at t=0 by an
external force of 288cos(4t) lb, determine the position of the mass
at any time. Assume that g=32 fts2. Solve for u in feet.
Enclose arguments of functions in parentheses. For example,
sin(2x).
If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 6 lb
and a spring constant 4 lbin is suddenly set in motion at t=0 by an
external force of 63cos(12t) lb, determine the position of the mass
at any time. Assume that g=32 fts2. Solve for u in feet.
If an undamped spring-mass system with a mass that weighs 24 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 24 lb
and a spring constant 16 lbin is suddenly set in motion at t=0 by
an external force of 432cos(8t) lb, determine the position of the
mass at any time. Assume that g=32 fts2. Solve for u in feet.
Enclose arguments of functions in parentheses. For example,
sin(2x).
u(t) = ?
1.) A mass-spring system consists of an object of mass 1 Kilogram connected to a spring...
1.) A mass-spring system consists of an object of mass 1
Kilogram connected to a spring with a stiffness of 9. The damping
constant is 6. Derive the function (1) that determines the distance
from the equilibrium point if the initial position is 3 meters from
the equilibrium point and the initial speed is 3 meters per
second.
a.) What is the maximum distance from the equilibrium point?
b.) Determine the general solution of the nonhomogeneous linear
differential
equation using...
A spring-mass system has a spring constant of 3 Nm. A mass of 2 kg is...
A spring-mass system has a spring constant of 3 Nm. A mass of 2
kg is attached to the spring, and the motion takes place in a
viscous fluid that offers a resistance numerically equal to the
magnitude of the instantaneous velocity. If the system is driven by
an external force of 9cos(3t)−6sin(3t) N,determine the steady-state
response in the form Rcos(ωt−δ).
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