An instrument package A is bolted to a shaker table as shown. The table moves vertically in simple harmonic motion at the same frequency as the variable-speed motor that drives it. The package is to be tested at a peak acceleration of 150 ft/s2. Knowing that the amplitude of the shaker table is 2.3 in., determine (a) the required speed of the motor in rpm, (b) the maximum velocity of the table.

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: Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be…

A: Given:P=38 NQ=52 NS=64 NT=31 Nα=15°β=65°θ=25°

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: In practice, it is often difficult to determine the logarithmic decrement of a system with light…

A: Consider a single degree of freedom spring mass damper system as shown in the figure below.

Q: A connecting rod supported by a knife-edge at point A. For si oscillations the angular acceleration…

A: To given thatα=-6θω at θ=22.4°          =22.4×π180rad is zerofor ωmax:dωdt=0…

Q: angular acceleration of the connecting rod is governed by the relationship α = -6.5θ where α is…

A:

Q: A certain toy “helicopter” or “whirlybird” consists simply of a propeller attached to a shaft that…

A: Given : Length - L Mass - m Angular speed - ω0 Moment of Inertia - 112mL2 To find : (a) Based on…

Q: The rotor of a gas turbine is spinning at a speed of 6,300 rpm when the turbine is deactivated. It…

A: Rotor initial speed Ni = 6300 rpm Rotor final speed Nf = 0 rpm ( rotor reaches rest )Time taken t =…

Q: A connecting rod is supported by a knife-edge at point A. For small oscillations the angular…

A:

Q: A connecting rod is supported by a knife-edge at point A. For small oscillations the angular…

A: Given data:To find:Angular position when t = 3 sec.

Q: A connecting rod is supported by a knife-edge at point A. For small oscillations the angular…

A: maximum angular velocity when t = 2sec.

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

A:

Q: The simple pendulum shown oscillates in the vertical plane (the plane of the figure) as the pendulum…

A:

Q: A toy battery-powered plane is hanging from the ceiling. With the motor turned off it is pulled to…

A:

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: 2. Tid the percentage mercase in specu, in the Danis rise by 20 min. [Alls. 370] A Porter governor…

A: Ball 1 mass, m=3 kg Ball 2 mass, M=15 kg Arm length, BP=BD=200mm =0.2m Minimum radius of rotation,…

Q: Determine the natural frequency of the system shown beside using Motion equation

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

A:

Q: In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, O"max,…

A: Given: θmax"θmax'= 2π  s-1 For an oscillatory motion of the simple pendulum, Velocity is given by,…

Q: A harmonic motion has a frequency of 30 cycle/second and its maximum velocity is 10 m/s. Determine…

A: Given:f=30 hzvmax=10 m/s

Q: A slider crank mechanism, FIG. A5, consists of a piston of 2.5 kg mass and a crank of 50 mm…

A:

Q: In simple harmonic motion, the maximum acceleration of a moving particle is expressed as O a. wr O…

A:

Q: QUESTION 1 The frequency of vibrations of a machine is 150HZ. Determine; a) Its frequency in rad/s…

A: We are suppose to solve only one question. Please post other question as a separate question.

Q: he passenger car is modeled on a quarter-car model, in which case each wheel has a mass of 390 kg,…

A:

Q: A connecting rod is supported by a knife-edge at point A. For small oscillations the angular…

A:

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

A:

Q: Derive Lagrange’s equation of motion from Newton’s laws.

A: Lagrange's equation of motion is a powerful mathematical tool that can be used to describe the…

Q: quantity of oil into the well pipe, and he column of oil is then lifted to obtain a discharge into…

A:

Q: Pull the pendulum ball from the equilibrium position to the positive direction of displacement, so…

A:

Q: Q. 1. Derive the equations of motion for the systems shown below. Also determine their natural…

A: Given : To find : Equation of motion Natural frequency

Q: An eccentric plate circular cam of 160 mm diameter and eccentricity 40 mm provides motion to a…

A: Given that, Diameter of cam, D=160 mm Radius of cam, r=D2=1602=80 mm Eccentricity, e=40 mm=0.04 m…

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

A:

Q: 1. At the state shown, the disk rotates about O in the counterclockwise direction at 4 rad/s. This…

A:

Q: A mass hanging from a vertical spring and a simple pendulum each have a period of oscillation of 1…

A:

Q: The rotor of a gas turbine is turning at a speed of 6,600 rpm when the turbine is turned off. It is…

A:

Q: (a) in

A: (a) when ball displace with angle θ then natuaral frequency for case 1st moment of inertia of disl…

Q: Question : The crank of a two cylinder, 90 degrees V-engine moves with simple harmonic motion. The…

A: The solution is

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

A:

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: 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: 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.

Q: (ii) A mass of 5 kg is attached to a spring and rests on a horizontal surface. The mass is then…

A: For spring mass system, Mass (m)= 5 kgTime period (T)= 1.2 secHorizontal displacement =10 mm=0.01 m…

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.