Thanks k2aFigure 12k,The mechanical system shown in Figure 1 consists of two springs attached to a pulley. The pulley hasa radius R and a mass moment of inertia J while the springs have spring constants 2k; and k2.Assuming ideal springs and neglecting the effect of gravity on the pulley.„Assuming kj=11 N/m, k2=8 N/m, a=5 m, J=38 kg.m?, and R=11 mFirst, draw the Free Body Diagram of the system and clearly label all forces acting in it. Second.derive the equations of motion of the system for small oscillations using Newton's second law in the:formEquation of Motion: b40 + b30 + b20 + b¡0 + bo . where 0 is the angle that represents.the pully rotation. Third, find the natural frequency of the system (w). :formEquation of Motlon: b40 + b30 +b½0 + b¡0 + bo , where 0 is the angle that represents.the pully rotation. Ihird. find the natural frequency of the system (w).„Finally, fill in the following blanks by the values of bi, and the natural freguency of the system (w)nNotes:1) The coefficient of the higher part of the equation should be 1Ex for third degree system: 6 + 46 + 20 + 50 + 3,Ex for secod degree system: 0 + 20 + 50 + 3,Ex for first degree system: 0 + 50 +31) You should fill the blanks with numbers only and with one decimal at max as EX: 12.12) The error is not cumulative and if you don't know any answer, just fill it with any randomnumber more than 1 (zero is not acceptable).1) The value of b,=2) The value of b3 =3) The value of b2 =

Answered: k2 R | bartleby

Engineering

Mechanical Engineering

k2 R

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter2: Axially Loaded Members

Section: Chapter Questions

Problem 2.2.12P: A small lab scale has a rigid L-shaped frame ABC consisting of a horizontal aim AB (length b = 30...

See similar textbooks

Similar questions

Consider the system formed by three ideal springs, a rigid rod of negligible mass and a body of mass M, as illustrated in the figure. The two springs attached to the ceiling are identical and have spring constant K1 = 2 kg/s2 and natural length L1 = 10 cm, while the third has spring constant K2 = 3 kg/s2 and natural length L2 = 20 cm. Assume that the mass M and the rod oscillate only along the vertical x-axis and that the gravitational acceleration is uniform with magnitude g=10 m/s2. What is the mass oscillation period? Choose the closest value.
Under some circumstances, when two parallel springswith constants k1 and k2 support a single mass, theeffective spring constant of the system is given byk 4k1k2/(k1 + k2). A mass weighing 20 pounds stretchesone spring 6 inches and another spring 2 inches. Thesprings are first attached to a common rigid supportand then to a metal plate. As the figure illustrates(see image), the mass is attached to the center of the plate in the distributiondouble spring. Determine the constant of theeffective spring for this system. find the equationof motion if the mass is initially released fromequilibrium position with downward speed of2 ft/sec.
For the double slider mechanism shown in the following figure, the crank OA rotates at a uniform speed of 24 rad/s ccw. we need to find the required torque for the crank, if two forces act at sliders B and C as shown in the figure. (P = 4 kN, Q = 2 kN). OA = 10 cm, AB = AC = 70 cm. mg = mc = 5 Kg. Neglect other links weights. (5) (2) (3) B (4) (6) C 45° X. The velocity of slip of slider B in m/s² = Choose.. + The velocity of slip of slider C in m/s? = Choose... + The acceleration of slip of slider B in m/s² = Choose.. + The acceleration of slip of slider C in m/s² = Choose.. + The magnitude of required torque for the crank in N.m = Choose..
Consider an electrical motor with mass M= 29 kg located at the tip of a rigid beam pivoted at point A, with the other end supported by a spring and damper with stiffness, k = 6 MN/m and damper c= 12 kNs/m, as shown in the figure below. Assume that the rigid beam is massless, the length is L= 1.3 m (horizontal distance between point O and pivot point A), and zero initial conditions. If there is an unbalanced mass of m0=2 kg in the rotating part of the motor, eccentricity is e =382 mm, and the rotor is rotating with a speed of w (omega) = 203 rad/s, determine the maximum amplitude response of point O at steady state condition in millimetre. Assume the line of actions of forces created by spring and damper act through point O, the centre of electric motor. Treat the electric motor mass as a point mass for calculating its moment of inertia about point A.
In the system shown in the figure, the spring stiffness k = 2 × 103 N/m and the total massof the system is m = 20 kg, the eccentric mass m0 = 0.2 kg, the eccentricity e = 0.1 m andthe rotation angular velocity of the unbalanced mass is ω1 = 20 rad/s. The applied force isF(t) = 15 sin ω2t with ω2 = 30 rad/s. Determine:(a) the steady state motion of the system;(b) the force transmitted in the spring and estimate the maximum value of the force
Suppose an automobile engine can produce 195 N⋅m of torque, and assume this car is suspended so that the wheels can turn freely. Each wheel acts like a 14 kg disk that has a 0.195 m radius. The tires act like 2.15-kg rings that have inside radii of 0.18 m and outside radii of 0.34 m. The tread of each tire acts like a 8.5-kg hoop of radius 0.335 m. The 16-kg axle acts like a solid cylinder that has a 1.75-cm radius. The 29.5-kg drive shaft acts like a solid cylinder that has a 3.25-cm radius. Calculate the angular acceleration, in radians per squared second, produced by the motor if 95.0% of this torque is applied to the drive shaft, axle, and rear wheels of a car.
Figure Q3(b) shows a uniform bar AB of mass = 8 kg hinged at point C. Point A is connected to a spring to maintain the bar in vertical direction, and the stiffness k = 500 N/m. If point A is displaced counter-clockwise by a small angle θ = 3.5 degree and released, (i) With the free body diagram and kinetic diagram, determine the initial horizontal displacement of A.
A wheel of mass m, radius r and radius of gyration k is rolling along a horizontal road with hub velocity v in the +ve x direction. Brakes are applied to the wheel, providing a torque of -M, slowing the vehicle to rest. Assuming that the wheel rolls without slipping and the hub position starts at x=0, where m = 10 kg, r = 0.85 m, k = 0.595 m, v = 5m/s, M = 21 Nm, g = 9.81 m/s^2 a) Find the constant acceleration, (ax) of the wheel hub b) Find the minimum static coefficient of friction (mu) between the road and the wheel c) Find the stopping distance (smax) and time (tmax)
A box of mass m = 0.7 kg is attached to a rope which is wrapped around a physical pulley with a radius of R = 10.2 cm and a rotational inertia of I = 0.075 kg·m2. When the box is released it starts to fall down with a constant acceleration and, at the same time, the pulley starts to spin up, see the picture below. Assuming that the pulley is frictionless, what is the magnitude of the box's acceleration and what is the tension in the rope? The acceleration of the box, a ? The tension in the rope, T? If the box starts from rest and traveled downwards a distance of h = 28 cm, what is the speed of the box and what is the angular velocity of the pulley? The speed of the box, v =? The angular velocity of the pulley, ω? -------------------------------------------------------------- A Merry Go Round carousel has a radius of R = 2.4 m and a rotational inertia of I = 695 kg·m2. A 75‑kg student is on the carousel at the midpoint between the carousel's center and the rim (at R/2 distance from…
In the figure below Atwood’s machine is drawn - two masses  and  hanging over a massive pulley of rotational inertia  and radius , connected by a massless unstretchable string. The string rolls on the pulley without slipping.a) Find the acceleration of the system and the tensions in the string on both sides of the pulley in terms of in terms of given variables.b) Why are the rope tensions on two sides of the pulley not the same? Explain it physically.c) Suppose mass    and the system is released from rest with the masses at equal heights. When mass  has descended a distance , find the velocity of each mass and the angular velocity of the pulley.[4***] A string is rolled around a cylinder(   kg) as shown in figure. A person pulls on the string, causing the cylinder to roll without slipping along the floor
An electric motor is accelerating a 250 kg load with acceleration of 1.2 m/s? througha gear box as shown Figure Q1(b). The rope that carries the load and spiral spring are encircled on a pulley with diameter 1.2m. Gear box ratio is 0. 1 and gear box efficiency is 100%, while gear box equivalent moment inertia is 5.55 km?. Neglect friction effect in this drive system and assume spiral spring force is X newtonCalculate the torque of the motor needed to bring up the load with acceleration1.2 m/s?.
Consider a disc of mass, M with radius 0.5 m on a slope with angle 45 degrees to the horizontal. It has a good grip on the slope and does not slip. The disc is constructed so that its mass per unit area, ρ(r) = r1/2 kg m−2, with r being the radial distance in metres from the axis of the disc. What is the equation describing the linear acceleration of the centre of mass of the disc down the slope in terms of the angular acceleration of the disc.