T = Tm sin oft

Q: Q4. An air-conditioning chiller unit weighing 5.0kg is to be supported by four air springs. Design…

A:

Q: The homogeneous disk, of mass-6Kg and radius R-1 m, rolls without slipping over the surface. The…

A: If you need any further assistance contact me by raising the clarification request

Q: The equilibrium position of the mass m = 3.8 kg occurs where y = 0 and YB = 0. When the attachment B…

A: Given data: mass of block (m) = 3.8 kg Spring stiffness (k) = 875 N/m

Q: 3. A light rod AB of length 600 mm has a fixed hinge at A and a mass of 5 kg concentrated at B. A…

A: The given information in the problem is shown in the following attached image:

Q: A 6-kg uniform cylinder can roll without sliding on a horizontal surface and is attached by a pin at…

A: Given Mass of the cylinder = 6 kg Mass of the bar = 4 kg Length of the bar = 12 mm = 0.012 m Spring…

Q: Two 40-g weights are attached at A and B to the rim of a 1.5-kg uniform disk of radius r = 100 mm.…

A: Consider the diagram shown below for the disc for a small angular displacement anticlockwise.

Q: 1. The displacement formulation for a plane truss is similar to that of a mass-spring system. The…

A: The stiffness matrix of the truss is…

Q: Determine the natural period of vibration of the uniform bar of mass m when it is displaced…

A: Consider the diagram shown below for the small angular displacement of the rod.

Q: natural frequency of the system.

A: Given: A mass of 1 kg, m=1 kgAttached to two identical springs each of stiffness;  k=25 kN/mUnder…

Q: A 64-lb block is attached to a spring with a constant of k = 1 kip/ft and can move without friction…

A: Given Data: The weight of the block is: w= 64 lb. The value of the spring constant is: k=1 kip/ft.…

Q: A 6-kg uniform cylinder can roll without sliding on a horizontal surface and is attached by a pin at…

A: GivenMass of the cylinder = 6 kgMass of the bar = 4 kgLength of the bar = 12 mm = 0.012 mSpring…

Q: A collar with mass m that slides on a frictionless horizontal rod is attached to a spring with…

A: The static deflection of the spring is The natural frequency of the system is The amplitude of the…

Q: Problem 5 The 60-kg block is suspended from the 12-kg pulley that has a radius of gyration about…

A: Write the given information. Write the expression of the mass moment of inertia of the pulley.

Q: 6. A spring with a spring constant of k = 2 is placed in a medium with a damping force numerically…

A: Given data: k=2 lb/ftβ=4 Need to determine the all values of "m" for which the subsequent free…

Q: Determine a natural frequency of vibration as a function of k₁, k₂. g and W of a spring-mass system…

A:

Q: Problem 4: A part of a machine of mass 4.54 kg has a reciprocating motion which is simple harmonic…

A: Given data:To find:The accelerating force and velocity when mass is at 75 mm from mid-stroke.The…

Q: n electric motor with a mass of 260 kg and a rotating nbalance, is mounted near the end of a steel…

A:

Q: 1. The uniform rod ABC weighs 5 lb, and is attached to wo springs as shown. If end C is given a…

A:

Q: Problem 5 The 60-kg block is suspended from the 12-kg pulley that has a radius of gyration about…

A: Write the given information. Write the expression of the mass moment of inertia of the pulley.

Q: A 30-kg rotor has an eccentricity of 1.2 cm. It is mounted on a shaft and bearing system whose…

A:

Q: A ship has a radius of gyration of k=8m, a transverse metacentric height GM of 2m and a displacement…

A: The radius of gyration, kxx = 8 mThe metacentric height, GM = 2 mThe displacement force, F = 156960…

Q: A 16.3 kg motor is bolted to a light horizontal beam which has a static deflection of 0.19 cm due to…

A: GIVEN DATA UNBALANCE MASS m=0.02 kg Eccentricity e=15.8cm SPEED N=900rpm We have to calculate…

Q: A large industrial cooling system of mass 160 kg is supported by six springs arranged in parallel.…

A:

Q: A 20 kg motor is bolted to a light horizontal beam which has a static deflection of 0.2 cm due to…

A:

Q: 1. A 20-lb uniform cylinder can roll without sliding on an incline and is attached to a spring AB as…

A:

Q: A 15-lb uniform cylinder can roll without sliding on an incline and is attached to a spring AB as…

A: Given data: Weight of the cylinder, W = 15 lb. Stiffness of the spring, k = 4.5 lb/in. = 54 lb/ft.…

Q: In the system shown,m= 2 kg, k= 1000 N/m, theta= 30 degrees and the friction coefficient between the…

A: Draw the free body diagram.

Q: Two 12-lb uniform disks are attached to the 20-lb rod AB as shown. Knowing that the constant of the…

A: At point A, the system is in the maximum displacement position. So, the system will be at rest. The…

Q: A bungee jumper weighing 160 lb ties one end of an elastic rope with a length of 200 ft and…

A: Natural frequency formula ω =km weight  = 160 lb stiffness k = 10 lb/in

Q: The 6-kg uniform rod AC is attached to springs of constant k = 500 N/m at B and k = 620 N/m at C,…

A:

Q: A spring is stretched to in. by a 4-1D weight. Let the weight be pulled down bin. below equilibrium…

A: To find: The equation of position of spring. Given: The initial Stretch in the spring is x0=6 in1…

Q: a. A pump rotor of total mass 350 kg has an unbalanced mass of 10 kg and can be modelled as a single…

A:

Q: A uniform disk with radius r and mass m  can roll without slipping on a cylindrical surface and is…

A: Let's displaced the point 'A' by a small displacement 'x' which makes a small angle 'θ' at point…

Q: A 7-kg block is suspended by three identical springs, each with k = 200 N/m. The bottom of the block…

A:

Q: The 100-lb platform A is attached to springs B and D, each of which has a constant k = 120 lb/ft.…

A: Given: Weight of platform A, wA=100 lb kB=kD=120 lb/ft the newly added weight is 80 lb. first case:…

Q: A mass of flexible machine part, m, of 10 × 1 kg was observed to vibrate badly at frequency of 10…

A:

Q: n in the Fig. 3, the CM of a cylinder SR is connected to the top of hoop of

A: The mass  if cylinder is .The radius of the cylinder is .The mass of the hoop is .The spring…

Q: k A k 30 ст С 1 W 60 cm

A: given; weight =Wmass(m)=weight(W)gBC=60cm=0.6mAB=30cm=0.3m

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.