2. Calculate the EOM (using Newtons 2nd law) and the natural frequency of the spring-mass system shown below. Each...
a)by using newtons 2nd law,derive the equation of
motion for the vibration system in matrix form
b)diferrentiate between the 1st,2nd and 3rd vibration modes
characteristic of the train system based on the mode shape
diagram
A three coaches train system shown in Figure 3(a) can be simplified as a three degree of freedoms semi definite mass-spring system as illustrated in Figure 3(b). The masses of the three coaches are /m = 15000 kg, m-10000 kg and m-15000 kg. The three...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m = 10 kg, and damping constant c-150 N-s/m. If the initial displacement is xo-o and the initial velocity is 10 m/s (1) Find the damping ratio. (2) Is the system underdamped or overdamped? Why? (3) Calculate the damped natural frequency (4) Determine the free vibration response of the system.
3. A spring-mass system has mass m, spring constant k, and hence natural frequency ω0 = (k/m)^1/2 . The damping constant can take any value. Show that the smallest half-life you can get without the spring becoming overdamped is (ln2 / ω0) .
For the spring-mass system shown below with the mass sliding on
a frictionless floor, A = 1.0 m, the spring constant k = 2.0 N/m,
and the mass m = 2.0 kg. The period of oscillation T is
QUESTION 18 For the spring-mass system shown below with the mass sliding on a frictionless floor, A = 1.0 m, the spring constant k = 2.0 N/m, and the mass m = 2.0 kg. The period of oscillation T is x= 0...
2. A spring is stretched 10 cm by a force of 3 newtons. A mass of 2 kg is hung from the spring and is also attached to a viscous damper that exerts a force of 3 newtons when the velocity of the mass is 5 m/sec. If the mass is pulled down 5 cm below its equilibrium position and given an initial downward velocity of 10 cm/sec, determine its position u at time t. Find the quasi frequency and...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mx+cx + kx = A sin(at) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor 5 and the un-damped natural frequency Using the given formulas for...
2. An undamped mass on a spring has a natural frequency of 10Hz. The system consists of four identical springs in parallel, and suffers some damage so that one spring is removed, and at the same time the mass is halved. Find the modified natural frequency (in Hz) of the system after damage. [5]
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2. (20 points) The damped single degree-of-freedom mass-spring system shown below has a mass m- 20 kg and a spring stiffness coefficient k 2400 N/m. a) Determine the damping coefficient of the system, if it is given that the mass exhibits a response with an amplitude of 0.02 m when the support is harmonically excited at the natural frequency of the system with an amplitude Yo-0.007 m b) Determine the amplitude of the dynamic...
Question 12 4 points Save A Find the Natural frequency for below system, if mass is 25 kg, and k is 7 N/m k 2k 4k k m 3k M
Problem 5: The spring-mass system shown has spring constants ky = 24 kN/m and kz = 36 kN/m with a suspended mass of 35 kg at A. If the block is displaced 50 mm below its equilibrium position and released with no initial velocity, determine: a) The circular natural frequency, the natural frequency, and the period b) The position, velocity, and acceleration of the block after a time of 30 seconds k2 mm ki A