2. An undamped spring-mass system with a mass of 1.3kg is observed to have a natural frequency of 90 cycles per second. What is the spring constant?
2. An undamped spring-mass system with a mass of 1.3kg is observed to have a natural...
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]
For a mass-spring oscillator, Newton's second law implies that the position y(t) of the mass is governed by the second-order differential equation my'' (t) + by' (t) + ky(t) = 0. (a) Find the equation of motion for the vibrating spring with damping if m= 10 kg, b = 100 kg/sec, k = 260 kg/sec?. y(0) = 0.3 m, and y'(0) = -0.4 m/sec. (b) After how many seconds will the mass in part (a) first cross the equilibrium point?...
Determine the value of the spring constant that would result in a spring-mass system that would execute one complete cycle of oscillation every 2 s, for a mass of 1 kg. What natural frequency does this system exhibit in radians/second?
2. Calculate the EOM (using Newtons 2nd law) and the natural frequency of the spring-mass system shown below. Each mass is m-5 kg and the linear elastic spring has a constant k 325 N/m. 2. Calculate the EOM (using Newtons 2nd law) and the natural frequency of the spring-mass system shown below. Each mass is m-5 kg and the linear elastic spring has a constant k 325 N/m.
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) .
If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant 1 lb/in is suddenly set in motion at t = 0 by an external force of 3 cos 7t lb, determine the position of the mass at any time. (Use g = 32 ft/s2 for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in feet of the mass from its equilibrium position at time t seconds.) u(t) = ft
The undamped natural frequency of the second-order low pass system may be identified as the frequency at which the phase shift = __________ degrees.
3. A compressor of mass 700 kg has undamped spring mountings which deflect by 0.5 mm under its weight. This compressor, on its mountings, is installed on a flexible floor whose mass of 1400 kg may be considered as concentrated below the compressor. The floor has negligible damping. The highest natural frequency of vertical vibration of this combined system must not exceed 1.5 times that of the compressor with its spring mountings on a rigid foundation. Find a suitable value...
(Undamped system) An iron ball of mass 10kg is attached to a spring having a spring constant of 3.6N/m. The ball is started in motion from rest (i.e., initial velocity is zero) by stretching the spring 0.7m from the equilibrium position with an exerted force f(t)=6.8e-t Assume there is no air resistance. a) Find the position of the ball as a function of time. b) Determine how far from the equilibrium position the ball will be after 15 seconds.
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mi+ci +kx- Asin(ot) 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 un-damped natural frequency on a. and the A second order mechanical system of a...