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A simplified model of a washing machine is shown. A bundle of wet clothes forms a weight
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Vector Mechanics For Engineers
- The maximum permissible recoil distance of a gun is specified as 0.5 m. If the initial recoil velocity is to be between 8 m/s and 10 m/s, find the mass of the gun and the spring stiffness of the recoil mechanism. Assume that a critically damped dashpot is used in the recoil mechanism and the mass of the gun has to be at least 500 kg.arrow_forwardAn electric motor and its base have a combined mass of M = 12 kg. Each of the four springs attached to the base has a stiffness k =480 kN/m and a viscous damping coefficient c. The unbalance of the motor is equivalent to a mass m =0.005 kg located at the distance e=90mm from the center of the shaft.When the motor is running at ω = 400 rad/s, its steady-state amplitude is 1.8 mm.Determine (a) the damping coefficient of each spring; and (b) the phase anglebetween the displacement of the motor and ωt.arrow_forwardA 7-kg block is suspended by three identical springs, each with k = 200 N/m. The bottom of the block is attached to a dashpot that provides a damping force of F= 50|M N, where v is in m/s. At t = 0 s, the block is given an initial velocity upward of 0.6 m/s from its equilibrium position. (a) What is the natural frequency of the system? (b) Show whether this is an underdamped, a critically damped, or an overdamped system. (c) What is the frequency of the damped system? (d) What is the amplitude of the damped oscillation?arrow_forward
- A rotating machine of 400 kg is similar to the system shown below. It operates at 3600 rpm (note: 1 rpm = 2π/60 rad/s). The machine is unbalanced such that its effect is equivalent to a 4 kg mass located 20 cm from the axis of rotation. An isolator with a spring stiffness of 8x106 N/m and a damping constant of 2x104 Ns/m is placed between the machine and the foundation. Determine the steady state response of the system. Find the force transmitted to the foundation and transmissibility of the isolator. Find the damping ratio of the system ζ . Find the transmissibility of the system, Tf. Find the frequency ratio of the system, β. Find the amplitude of the harmonic excitation force of the system, Fo in Newton (N). Find the displacement amplitude of the steady state response of the system, X in millimeters (mm). Find the damped frequency of the system, ωd in rad/s. Find the force transmitted to the foundation, FT in Newton (N). Find the frequency of the harmonic…arrow_forwardA weight of 32 pounds is suspended from a spring with a modulus of 5 lb/ft. From equilibrium position, the weight is pulled down 4 inches below and then released. Given that the damping force in pounds is numerically equal to four times the instantaneous velocity, what is the position of the weight after sec.arrow_forward6. A spring with a spring constant of k = 2 is placed in a medium with a damping force numerically equal to 4 times the instantaneous velocity. If an object of mass m is suspended from the spring, determine all values of m for which the subsequent free motion will be non-oscillatory.arrow_forward
- A machine of mass 220 kg is mounted on the middle of a fixed-fixed beam, with a viscous damping mechanism not shown. The steel beam (E= 207 GPa) has the following dimensions: a=0.05m, b=0.2 m and L-4m. It has been observed that when a harmonic force of magnitude 1000N is applied, the maximum steady-state response occurred at a frequency of 700 rpm. Determine the equivalent damping constant, neglecting the mass of the beam. ㅏㅏ 1 = 4/ 7919 s/m 9129 N s/m O7007 Ns/m O 6807 Ns/m O F(t) = F, cos cot m u x(1)arrow_forwardA vehicle is modelled as a combined mass-spring-damper system that oscillates in the vertical direction only. The driver of the vehicle travels along a road whose elevation varies sinusoidally as shown in Figure 2. The mass of the vehicle, which includes the driver, is 2500 kg. The stiffness and damping of the shocks are 40 kN/m and 3000 kg/s respectively. i. Determine the amplitude of vibration of the vehicle when it travels at a constant speed of 90 km/hr along the sinusoidal road. y/m 0.6 ►Velocity of vehicle m 0.4 ► Rigid massless tyre 0.2 distance (m) 20 60 80 -0.2 Figure 2arrow_forwardA vehicle is modelled as a combined mass-spring-damper system that oscillates in the vertical direction only. The driver of the vehicle travels along a road whose elevation varies sinusoidally as shown in Figure 2. The mass of the vehicle, which includes the driver, is 2500 kg. The stiffness and damping of the shocks are 40 kN/m and 3000 kg/s respectively. i. Determine the amplitude of vibration of the vehicle when it travels at a constant speed of 90 km/hr along the sinusoidal road. ii. If additional load having a combined mass of 1000 kg is placed in the vehicle, determine the travelling speed of the vehicle that would result in a resonant condition. What is the amplitude of the vehicle at resonance? Using an appropriate graph and suitable equations, explain how the oscillations of the vehicle can be significantly reduced when travelling at very high speeds. Please note that a simple graphical sketch with your pen that clearly identifies the key points is acceptable. Your axes must…arrow_forward
- A mass of 1 slug is attached to a spring whose constant is 25 /4 lb /ft. Initially the mass is released 1 ft above the equilibrium po-sition with a downward velocity of 3 ft/ sec, and the subsequent motion takes place in a medium that offers a damping force nu-merically equal to 3 times the instantaneous velocity. An external force ƒ(t) is driving the system, but assume that initially ƒ(t) = 0.Formulate and solve an initial value problem that models the given system. Interpret your results.arrow_forward6. A machine of mass m = 2kg is supported by four springs and a damper of coefficient of damping c = 1 N.s/m, as shown in Figure 6. It is observed that the equilibrium position is established after the springs have depressed by 24.5 mm under the weight of the machine. At time t = 0, the machine is pushed down from its equilibrium position by y = 100mm , as shown, and then released. (a) For the system, (i) Calculate the total stiffness, k7, of the four springs and the natural circular frequency of vibration, 0, , (ii) The damping ratio, 5, and hence identify the prevailing type of Damping.arrow_forward6. A machine of mass m = 2kg is supported by four springs and a damper of coefficient of damping c = 1 N.s/m, as shown in Figure 6. It is observed that the equilibrium position is established after the springs have depressed by 24.5 mm under the weight of the machine. At time t = 0 , the machine is pushed down from its equilibrium position by y = 100mm , as shown, and then released. (a) For the system, (i) Calculate the total stiffness, kr, of the four springs and the natural circular frequency of vibration, @, , (ii) The damping ratio, 5 , and hence identify the prevailing type of Damping. (b) For the ensuing vibration of the machine, (i) Sketch the appropriate amplitude-time curve, and (ii) Determine the displacement of the machine from its equilibrium position after 5 oscillations. Equilibrium position y = 100mm k C Figure 6arrow_forward
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