QUESTION 3
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An L-shaped rigid bar is attached with a pivot to a wall as shown in the figure below. Assume that the L-shaped rigid bar is massless. A mass of m = 9.1958 kg is attached to one end of the rigid bar and the other end is supported by spring k = 965.7083 N/m and damper c = 121.3183 Ns/m. Determinate the steady state amplitude of mass m, given
where F0 =417.8427 N, ω = 48.0443 rad/s, and
dimensions are a =0.2149 m, b = 0.0890 m. Note:
assume that the system is vibrating in horizontal plane (this means
that gravity will not affect the response of the system).
a. 43.4450 mm
b. 0.0184 mm
c. 203.3941 mm
d. 18.3839 mm
e. 79.0409 mm
where F0 =417.8427 N, ω = 48.0443 rad/s, and
dimensions are a =0.2149 m, b = 0.0890 m. Note:
assume that the system is vibrating in horizontal plane (this means
that gravity will not affect the response of the system).
Homework Answers
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QUESTION 3
An L-shaped rigid bar is attached with a pivot to a wall as
shown...
A rigid bar with mass m and length L is pivoted at the fixed point O....
A rigid bar with mass m and length L is pivoted at the fixed point O. A small disk of mass M is attached at the upper end of the bar. The disk is attached to a spring of stiffness k and a viscous damper with damping constant c. The moment of inertia of the bar about point O is Io M2/3 and the spring is unstretched when the bar is vertical. rs Under what condition is the vertical position...
b Write an expression for the tension T in the horizontal cable AB 25% Part (c)...
b Write an expression for the
tension T in the horizontal cable AB
25%
Part (c) Write an expression for the x-component
Px of the force exerted by the pivot on the
beam, in terms of T.
25%
Part (d) What is the tension in the horizontal cable, in
newtons, if the mass of the beam is 34 kg, the length of the beam
is 11 m, and the angle is 28°?
A uniform beam of length L
and mass...
The bar ABC is attached to the vertical rod with a horizontal pin. The essembly is...
The bar ABC is attached to the vertical rod with a horizontal
pin. The essembly is free to rotate about the axis of the rod. in
the absence of friction, the equations of motion of the system
are
If the system is set into motion with the initial conditions
and
, obtain a numerical solution with the adaptive Runger-Kutta
method from
to
and plot
vs.
B A o 0 = 62 sin 8 cose We were unable to transcribe this...
A ball of mass M is attached to one end of a spring of stiffness k...
A ball of mass M is attached to one end of a spring of
stiffness k and relaxed length
L0. The other end of the spring
is attached to the ceiling. When the ball hangs at rest in
equilibrium at the end of the spring it is located at the origin of
the coordinate system shown and the spring’s length is
Leq.
a. The figure shows the ball at position . What are the components of the
vector Li that...
Please explain the solution 3. A massless rope of length l, attached toa fixed pivot at...
Please explain the solution
3. A massless rope of length l, attached toa fixed pivot at one end and with a mass m at the other end, is held horizontally and then released, as shown in the diagram. When the mass is at its lowest point, the tension in the rope is (A) 0 (B) gl/2 (C) mg (D) 2mg (E) 3mg
A block of mass m is attached by means of a spring of constant to a...
A block of mass m is attached by means of a spring of constant
to a wedge of mass
and height
that forms an angle
with the horizontal, as shown in the figure. Mass
can slide on the horizontal surface. Note: don't consider
friction.
a) Calculate the frequencies of small oscillations of the system
around equilibrium.
b) Find and schematically draw the relative configurations of the
normal modes corresponding to each frequency of the system.
We were unable to transcribe...
Figure Q1 illustrates a simple pressure relief valve system, which consists of a rigid L-shaped beam,...
Figure Q1 illustrates a simple pressure relief valve system, which consists of a rigid L-shaped beam, hinged at a point where the horizontal part of the beam has length 2L and the vertical part has length L. A spring of stiffness k is attached midway along the horizontal part of the beam, and a damper with damping coefficient c is attached to the vertical part of the beam, at a distance 0.75L from the hinge, O. The pressure relief valve...
1. Springs and a mass are attached to a rigid bar, as shown in Fig 1....
1. Springs and a mass are attached to a rigid bar, as shown in Fig 1. The hinges are free to rotate. 0 denotes the rotational angle of the rod, and 0-0 when all springs are not stretched. The mass of the bar and the size of the mass are negligible. Neglect gravitational force, and assume 0 is very small. 1) Derive the equation of motion for this system with Lagrange's method. (20pt) 2) Find the natural frequency of the...
A massless rigid rod whose length L = 21.0 cm has a ball of mass m...
A massless rigid rod whose length L = 21.0 cm has a ball of mass
m = 0.079 kg attached to one end (see Figure). The other end is
pivoted in such a way that the ball will move in a vertical circle.
The system is launched from the horizontal position A with an
initial downward speed v0. The ball just reaches point D
and then stops. Calculate v0.
What is the tension in the rod at B?
· Rod...
An L-shaped rigid body ABC consists of two identical uniform slender rods, each of mass 40 kg and...
An L-shaped rigid body ABC consists
of two identical uniform slender rods, each of mass 40
kg and of length, L= 1.6
m welded together. The rigid body is pinned at its
vertex B as shown, with the
end C attached to a spring with a spring
constant, 6 N/cm .
PART A - Determine the natural cycle frequency of the
system.
PART B - If during the oscillatory motion the
end A is observed to move with a speed of 0.12
m/s when AB is vertical,
what...
A rigid bar with mass m and length L is pivoted at the fixed point O. A small disk of mass M is attached at the upper end of the bar. The disk is attached to a spring of stiffness k and a viscous damper with damping constant c. The moment of inertia of the bar about point O is Io M2/3 and the spring is unstretched when the bar is vertical. rs Under what condition is the vertical position...
b Write an expression for the
tension T in the horizontal cable AB
25%
Part (c) Write an expression for the x-component
Px of the force exerted by the pivot on the
beam, in terms of T.
25%
Part (d) What is the tension in the horizontal cable, in
newtons, if the mass of the beam is 34 kg, the length of the beam
is 11 m, and the angle is 28°?
A uniform beam of length L
and mass...
The bar ABC is attached to the vertical rod with a horizontal
pin. The essembly is free to rotate about the axis of the rod. in
the absence of friction, the equations of motion of the system
are
If the system is set into motion with the initial conditions
and
, obtain a numerical solution with the adaptive Runger-Kutta
method from
to
and plot
vs.
B A o 0 = 62 sin 8 cose We were unable to transcribe this...
A ball of mass M is attached to one end of a spring of
stiffness k and relaxed length
L0. The other end of the spring
is attached to the ceiling. When the ball hangs at rest in
equilibrium at the end of the spring it is located at the origin of
the coordinate system shown and the spring’s length is
Leq.
a. The figure shows the ball at position . What are the components of the
vector Li that...
Please explain the solution
3. A massless rope of length l, attached toa fixed pivot at one end and with a mass m at the other end, is held horizontally and then released, as shown in the diagram. When the mass is at its lowest point, the tension in the rope is (A) 0 (B) gl/2 (C) mg (D) 2mg (E) 3mg
A block of mass m is attached by means of a spring of constant
to a wedge of mass
and height
that forms an angle
with the horizontal, as shown in the figure. Mass
can slide on the horizontal surface. Note: don't consider
friction.
a) Calculate the frequencies of small oscillations of the system
around equilibrium.
b) Find and schematically draw the relative configurations of the
normal modes corresponding to each frequency of the system.
We were unable to transcribe...
Figure Q1 illustrates a simple pressure relief valve system, which consists of a rigid L-shaped beam, hinged at a point where the horizontal part of the beam has length 2L and the vertical part has length L. A spring of stiffness k is attached midway along the horizontal part of the beam, and a damper with damping coefficient c is attached to the vertical part of the beam, at a distance 0.75L from the hinge, O. The pressure relief valve...
1. Springs and a mass are attached to a rigid bar, as shown in Fig 1. The hinges are free to rotate. 0 denotes the rotational angle of the rod, and 0-0 when all springs are not stretched. The mass of the bar and the size of the mass are negligible. Neglect gravitational force, and assume 0 is very small. 1) Derive the equation of motion for this system with Lagrange's method. (20pt) 2) Find the natural frequency of the...
A massless rigid rod whose length L = 21.0 cm has a ball of mass
m = 0.079 kg attached to one end (see Figure). The other end is
pivoted in such a way that the ball will move in a vertical circle.
The system is launched from the horizontal position A with an
initial downward speed v0. The ball just reaches point D
and then stops. Calculate v0.
What is the tension in the rod at B?
· Rod...
An L-shaped rigid body ABC consists
of two identical uniform slender rods, each of mass 40
kg and of length, L= 1.6
m welded together. The rigid body is pinned at its
vertex B as shown, with the
end C attached to a spring with a spring
constant, 6 N/cm .
PART A - Determine the natural cycle frequency of the
system.
PART B - If during the oscillatory motion the
end A is observed to move with a speed of 0.12
m/s when AB is vertical,
what...
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