5 kN/m 12 kg

Q: (a) Magnitude of the position (in terms of A) of the oscillating mass when it's speed is 60% of it's…

A: here, velocity at extreme end will be zero so, total energy of system at extreme end will be…

Q: Determine the oscillations of a system with two degrees is L = (x² + y²) - w²(x² + y²)

A:

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: A mass-spring-damper system, with constants m=6.5 kg, c=12N*s/m y k=6.5 N/m, It is released from…

A:

Q: The period of vibration of the system shown is observed to be 0.6 s. After cylinder B has been…

A: Given T1 = 0.6 s T2 = 0.5 s MB = 3lb To find The weight of cylinder A The constant of the spring

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: An automobile manufacturer is testing the suspension system of their latest car model. They load the…

A:

Q: A mass weighing 8 lbs. stretches a spring 24 inches. Assuming that a damping force numerically…

A:

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: an object whose weight is 3 pounds, is placed on a spring and stretched 6 inches. When it reaches…

A: For solution refer below images.

Q: A close-coiled helical spring undergoes a static deflection of 30 mm when a mass of 2.5 kg is placed…

A:

Q: A vibrometer used to measure the amplitude of vibrations consists essentially of a box containing a…

A: For the steady-state motion of the system, the solution can be given as,

Q: amplitude of 50 mm, what is the maximum If the block is moved horizontally rightward from A 12 kg…

A: Springs are one of the flexible machine elements, which gets deformed when load is applied to it and…

Q: A 2-kg block is suspended from a spring having a stiffness of 800 N/m. If the block is given an…

A:

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

A:

Q: A homogeneous wire of length 2l is bent as shown and allowed to oscillate about a frictionless pin…

A: Given data: The length of the wire is 2l. The period of oscillation when the angle β = 0 is ? = ?0 .…

Q: A mass m that slides on a rough horizontal surface is attached to a spring of elastic constant k…

A: Let the mass of the body = mLet the spring constant of the body = kThe coefficient of friction of…

Q: Determine the natural frequency of a pendulum whose length is 5 m.

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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: Determine the period of small oscillations of a small particle that moves without friction inside a…

A:

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: 0.2-kg mass on a spring executes simple harmonic motion at a frequency f. What mass is necessary for…

A:

Q: A small ball of mass m attached at the midpoint of a tightly stretched elastic cord of length l can…

A: Let, Tension in the cord = T Mass of the ball = m Acceleration of the ball = x¨ Length of the…

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: The homogeneous rod OA is supported at point 0, and a mass of 2m is attached at the bottom of the…

A: A system consists both potential energy U and kinetic energy K,  according to law of conservation of…

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 40 kg motor is bolted to a light horizontal beam which has a static deflection of 0.2 cm due to…

A: GIVEN DATA UNBALANCE MASS m=0.02kg eccentricity e=16cm SPEED N=2400rpm   WE HAVE TO CALCULATE…

Q: A particle moves in simple harmonic motion. Knowing that the amplitude is 15 in. and the maximum…

A: Given data: The amplitude is xm = 15 in. The maximum acceleration is, a = 15 ft/s2. Calculate the…

Q: An object is in simple harmonic motion, Its angular velocity was 1.7 rev/s and the maximum…

A:

Q: An 8-kg uniform disk of radius 200 mm is welded to a vertical shaft with a fixed end at B. The disk…

A: Given Data Mass of the uniform disk, M=8 kg Radius of the uniform disk, R=0.2m

Q: The amplitude of motion in the undamped system is diminishes with time to be then zero Ture False O

A: The general equation of motion for undamped free vibration is given by, x=X e-ζ ωnt×sin(ωd+φ)where,X…

Q: A particle moves in simple harmonic motion. Knowing that the maximum velocity is 200 mm/s and the…

A: Given Data Vmax=200 mm/s=0.2 m/samax=4 m/s2

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

Q: Determine the natural vibration of a simple pendulum whose length is 5ft. * O 1.4 ft/s O 0.394 ft/s…

A: for simple pendulum, w = sqrt(g/l) here  g = gravity acceleration = 32.174 ft/s^2          l = 5 ft.

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.