
Concept explainers
(a)
Then the distance ‘d’ to maximise the frequency of oscillation when a small initial displacement is given.

Answer to Problem 19.50P
Distance
Explanation of Solution
Given information:
Mass of collar
Mass of rod
Length of rod
The forces corresponding to the rod and collar are shown in the free body diagram below:
Now, from the equation of motion taking moment about A,
And, moment of inertia of rod is
Compare the above equation with un-damped equation of vibration:
Natural frequency:
To maximise the frequency, we need to take the derivative with respect to d and set it equal to zero.
By solving the above equation we get,
Conclusion:
The distance
(b)
The period of oscillation.

Answer to Problem 19.50P
Period of vibration,
Explanation of Solution
Given information:
Mass of collar
Mass of rod
Length of rod
The forces corresponding to the rod and collar are shown in the free body diagram below:
Now, from the equation of motion taking moment about A,
And, moment of inertia of rod is
Compare the above equation with un-damped equation of vibration;
Natural frequency:
To maximise the frequency, we need to take the derivative with respect to d and set it equal to zero.
By solving the above equation we get,
Thus,
Now, natural frequency:
Then, Time period
Want to see more full solutions like this?
Chapter 19 Solutions
Vector Mechanics for Engineers: Dynamics
- (Read image)arrow_forward(Read Image)arrow_forwardM16x2 grade 8.8 bolts No. 25 C1- Q.2. The figure is a cross section of a grade 25 cast-iron pressure vessel. A total of N, M16x2.0 grade 8.8 bolts are to be used to resist a separating force of 160 kN. (a) Determine ks, km, and C. (b) Find the number of bolts required for a load factor of 2 where the bolts may be reused when the joint 19 mm is taken apart. (c) with the number of bolts obtained in (b), determine the realized load factor for overload, the yielding factor of safety, and the separation factor of safety. 19 mmarrow_forward
- Problem4. The thin uniform disk of mass m = 1-kg and radius R = 0.1m spins about the bent shaft OG with the angular speed w2 = 20 rad/s. At the same time, the shaft rotates about the z-axis with the angular speed 001 = 10 rad/s. The angle between the bent portion of the shaft and the z-axis is ẞ = 35°. The mass of the shaft is negligible compared to the mass of the disk. a. Find the angular momentum of the disk with respect to point G, based on the axis orientation as shown. Include an MVD in your solution. b. Find the angular momentum of the disk with respect to point O, based on the axis orientation as shown. (Note: O is NOT the center of fixed-point rotation.) c. Find the kinetic energy of the assembly. z R R 002 2R x Answer: H = -0.046ĵ-0.040 kg-m²/sec Ho=-0.146-0.015 kg-m²/sec T 0.518 N-m =arrow_forwardProblem 3. The assembly shown consists of a solid sphere of mass m and the uniform slender rod of the same mass, both of which are welded to the shaft. The assembly is rotating with angular velocity w at a particular moment. Find the angular momentum with respect to point O, in terms of the axes shown. Answer: Ñ。 = ½mc²wcosßsinßĵ + (}{mr²w + 2mb²w + ½ mc²wcos²ß) k 3 m r b 2 C لا marrow_forwardOnly question 2arrow_forward
- Only question 1arrow_forwardOnly question 3arrow_forwardI have Euler parameters that describe the orientation of N relative to Q, e = -0.7071*n3, e4 = 0.7071. I have Euler parameters that describe the orientation of U relative to N, e = -1/sqrt(3)*n1, e4 = sqrt(2/3). After using euler parameter rule of successive rotations, I get euler parameters that describe the orientation of U relative to Q, e = -0.4082*n1 - 0.4082*n2 - 0.5774*n3. I need euler parameters that describe the orientation of U relative to Q in vector basis of q instead of n. How do I get that?arrow_forward
- Describe at least 4 processes in engineering where control charts are (or should be) appliedarrow_forwardDescribe at least two (2) processes where control charts are (or should be) applied.arrow_forwardProblem 3: A cube-shaped spacecraft is in a circular Earth orbit. Let N (n,) be inertial and the spacecraft is denoted S (ŝ₁). The spacecraft is described such that ¯½º = J ŝ₁ŝ₁ + J ŝ₂§₂ + J §¸Ŝ3 Location of the spacecraft in the orbit is determined by the orbit-fixed unit vectors ê, that are oriented by the angle (Qt), where is a constant angular rate. 52 €3 3> 2t 55 Λ Из At the instant when Qt = 90°, the spacecraft S is oriented relative to the orbit such that 8₁ = 0° Space-three 1-2-3 angles 0₂ = 60° and ES = $₂ rad/s 0₁ = 135° (a) At this instant, determine the direction cosine matrix that describes the orientation of the spacecraft with respect to the inertial frame N.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY





