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3. The mass of the uniform, rigid, slender rod, shown in Figure 3, is small compared...
Learning Goal: To study the undamped vibration of a rigid body. A slender, uniform metal rod...
Learning Goal:
To study the undamped vibration of a rigid body.
A slender, uniform metal rod of mass m and length
l is pivoted without friction about an axis through its
midpoint and in a direction that is perpendicular to the rod. A
massless horizontal spring, with spring constant k, is
attached to the lower end of the rod; the other end of the spring
is attached to a rigid support. (Figure 1)
Part C) What is ωn, the angular...
The mass of the uniform slender steel rod, shown in Figure 2, is 3 kg. The...
The mass of the uniform slender steel rod, shown in Figure 2, is 3 kg. The system is set in motion with small oscillations about the horizontal equilibrium position shown. (i) Determine the position x for the slider such that the system period is 1 s. (ii) When the pivot is replaced by a built-in support that restricts any rotation at O and the spring is moved to the right-hand end with the 1.2 kg mass removed, calculate the frequency...
A slender, uniform metal rod of mass M and length l is pivoted without friction about an axis through its midpoint and p...
A slender, uniform metal rod of mass M and length l is pivoted
without friction about an axis through its midpoint and
perpendicular to the rod. A horizontal spring, assumed massless and
with force constant k, is attached to the lower end of the rod,
with the other end of the spring attached to a rigid support.
(Figure 1)
2. Find the torque τ due to the spring. Assume that θ is small
enough that the spring remains effectively horizontal...
Pendulum A is a physical pendulum made from a thin, rigid, and uniform rod whose length is d. One end of this rod is at...
Pendulum A is a physical pendulum made from a thin, rigid, and uniform rod whose length is d. One end of this rod is attached to the ceiling by a frictionless hinge, so the rod is free to swing back and forth. Pendulum B is a simple pendulum whose length is also d. Obtain the ratio TA/TB of their periods for small-angle oscillations.
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...
Q4 A ring of mass M and radius R is attached so that it can pivot asone of a rod of mass M and length 2R. the syste...
Q4 A ring of mass M and radius R is attached so that it can pivot asone of a rod of mass M and length 2R. the system is suspended by a pin at the other end of the rod and all in a uniform gravitational field,g; thus forming a double pendulum. The motion is restricted to a plane A) Show that the kinetic energy and potential energy can be written for small oscillations as: B) Find the natural frequencies...
3. The uniform rod of length 4b = 0.8 m and mass m = 2 kg...
3. The uniform rod of length 4b = 0.8 m and mass m = 2 kg is bent into the shape shown. The diameter of the rod is small compared with its length. Determine the moments of inertia of the rod about the three coordinate axes. (For a slender rod of mass m and length L, I = ml?)
The small sliders A and B are connected by the rigid slender rod. If the velocity...
The small sliders A and B are connected by the rigid slender rod. If the velocity of slider B is 1.58 m/s to the right and is constant over a certain interval of time, determine the speed of slider A when the system is in the position shown 2.51R 2.22 Answer: vA m/s
The uniform slender rod shown below has a mass of 15.0 kg and a length of...
The uniform slender rod shown below has a mass of 15.0 kg and a length of 2.50 m. It is free to spin about an axis through point A which is perpendicular to the page. A force of 10.5 N is applied at point P and is perpendicular to the rod. a) Calculate the angular acceleration of the rod about axis A due to the force applied at point P. b) If point A is moved to the end of...
Figure 3 Uniform disk Uniform rod 3) Figure 3 illustrates a physical pendulum comprising a uniform disk having mass M and radius R and a rod having the length R and mass M. The disk is pivotally m...
Figure 3 Uniform disk Uniform rod 3) Figure 3 illustrates a physical pendulum comprising a uniform disk having mass M and radius R and a rod having the length R and mass M. The disk is pivotally mounted with a friction-less horizontal axis of rotation that extends through the center of mass of the disk. The rod is fixedly attached to the edge of the disk and it extends vertically downward when the pendulum is in a state of static...
Learning Goal:
To study the undamped vibration of a rigid body.
A slender, uniform metal rod of mass m and length
l is pivoted without friction about an axis through its
midpoint and in a direction that is perpendicular to the rod. A
massless horizontal spring, with spring constant k, is
attached to the lower end of the rod; the other end of the spring
is attached to a rigid support. (Figure 1)
Part C) What is ωn, the angular...
The mass of the uniform slender steel rod, shown in Figure 2, is 3 kg. The system is set in motion with small oscillations about the horizontal equilibrium position shown. (i) Determine the position x for the slider such that the system period is 1 s. (ii) When the pivot is replaced by a built-in support that restricts any rotation at O and the spring is moved to the right-hand end with the 1.2 kg mass removed, calculate the frequency...
A slender, uniform metal rod of mass M and length l is pivoted
without friction about an axis through its midpoint and
perpendicular to the rod. A horizontal spring, assumed massless and
with force constant k, is attached to the lower end of the rod,
with the other end of the spring attached to a rigid support.
(Figure 1)
2. Find the torque τ due to the spring. Assume that θ is small
enough that the spring remains effectively horizontal...
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...
Q4 A ring of mass M and radius R is attached so that it can pivot asone of a rod of mass M and length 2R. the system is suspended by a pin at the other end of the rod and all in a uniform gravitational field,g; thus forming a double pendulum. The motion is restricted to a plane A) Show that the kinetic energy and potential energy can be written for small oscillations as: B) Find the natural frequencies...
3. The uniform rod of length 4b = 0.8 m and mass m = 2 kg is bent into the shape shown. The diameter of the rod is small compared with its length. Determine the moments of inertia of the rod about the three coordinate axes. (For a slender rod of mass m and length L, I = ml?)
The small sliders A and B are connected by the rigid slender rod. If the velocity of slider B is 1.58 m/s to the right and is constant over a certain interval of time, determine the speed of slider A when the system is in the position shown 2.51R 2.22 Answer: vA m/s
The uniform slender rod shown below has a mass of 15.0 kg and a length of 2.50 m. It is free to spin about an axis through point A which is perpendicular to the page. A force of 10.5 N is applied at point P and is perpendicular to the rod. a) Calculate the angular acceleration of the rod about axis A due to the force applied at point P. b) If point A is moved to the end of...
Figure 3 Uniform disk Uniform rod 3) Figure 3 illustrates a physical pendulum comprising a uniform disk having mass M and radius R and a rod having the length R and mass M. The disk is pivotally mounted with a friction-less horizontal axis of rotation that extends through the center of mass of the disk. The rod is fixedly attached to the edge of the disk and it extends vertically downward when the pendulum is in a state of static...
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