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 frequency of oscillations of the rod?
Homework Answers
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Learning Goal:
To study the undamped vibration of a rigid body.
A slender, uniform metal rod...
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...
A Pivoting Rod on a Spring - (full respect) help..
A slender, uniform metal rod of mass and length is pivoted without friction about an axisthrough its midpoint and perpendicularto the rod. A horizontalspring, assumed massless and with force constant , is attached to the lower end of the rod, withthe other end of the spring attached to a rigid support.(a) We start by analyzing the torques acting on the rod when it isdeflected by a small angle from the vertical. Considerfirst the torque due to gravity. Which of the...
3. The mass of the uniform, rigid, slender rod, shown in Figure 3, is small compared...
3. The mass of the uniform, rigid, slender rod, shown in Figure 3, is small compared to the mass attached to it. For small oscillations, calculate the natural frequency of swing of the mass. 77 Figure 3
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...
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...
Problem 9 (15 points) A 20-lb slender rod AB is 5 ft long and is pivoted about a point O which is...
Problem 9 (15 points) A 20-lb slender rod AB is 5 ft long and is pivoted about a point O which is 1 ft from end B. The other end is pressed against a spring of constant k-400 lbin until the spring is compressed 2 in, and the rod is in a horizontal position. If the rod is released from this position, determine its angular velocity and the reaction at the pivot O as the rod passes through a thirty...
D L/2 G L/2 B MO A uniform slender rod of mass M=10 kg and length...
D L/2 G L/2 B MO A uniform slender rod of mass M=10 kg and length L=3m, is hinged at A. The rod is held in a horizontal position against А the spring (k= 200kN/m) at G, the spring being in compression. When the rod is released from this horizontal position k Rigid (the spring is not connected to the rod), support it will rotate about the frictionless hinge Spring A in a vertical plane. Determine: support a. The minimum...
5-L1 Equilibrium of a Rigid Body Learning Goal: To analyze a rod assembly in three-dimensional space...
5-L1 Equilibrium of a Rigid Body Learning Goal: To analyze a rod assembly in three-dimensional space and determine the support reactions by using the equations of equilibrium for a rigid body The rod assembly shown has smooth journal bearings at A and C. The forces F1 = 500 N F = 450 N F = 490 N. and F, 800 N are applied as shown in the figure. The geometry of the rod assembly is given as a = 0.950...
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...
A rigid, massless rod has three particles with equal masses attached to it as shown in Figure P8.59.
A rigid, massless rod has three particles with equal masses attached to it as shown in Figure P8.59. The rod is free to rotate in a vertical plane about a friction-less axle perpendicular to the rod through the point Pand is released from rest in the horizontal position at t - 0. Assuming m and d are known, find (a) the moment of inertia of the system (rod plus particles) about the pivot, (b) the torque acting on the system...
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...
3. The mass of the uniform, rigid, slender rod, shown in Figure 3, is small compared to the mass attached to it. For small oscillations, calculate the natural frequency of swing of the mass. 77 Figure 3
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...
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...
Problem 9 (15 points) A 20-lb slender rod AB is 5 ft long and is pivoted about a point O which is 1 ft from end B. The other end is pressed against a spring of constant k-400 lbin until the spring is compressed 2 in, and the rod is in a horizontal position. If the rod is released from this position, determine its angular velocity and the reaction at the pivot O as the rod passes through a thirty...
D L/2 G L/2 B MO A uniform slender rod of mass M=10 kg and length L=3m, is hinged at A. The rod is held in a horizontal position against А the spring (k= 200kN/m) at G, the spring being in compression. When the rod is released from this horizontal position k Rigid (the spring is not connected to the rod), support it will rotate about the frictionless hinge Spring A in a vertical plane. Determine: support a. The minimum...
5-L1 Equilibrium of a Rigid Body Learning Goal: To analyze a rod assembly in three-dimensional space and determine the support reactions by using the equations of equilibrium for a rigid body The rod assembly shown has smooth journal bearings at A and C. The forces F1 = 500 N F = 450 N F = 490 N. and F, 800 N are applied as shown in the figure. The geometry of the rod assembly is given as a = 0.950...
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...
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