Question

In: Physics

A mass is connected by means of a spring to an inelastic support. The static deflection...

A mass is connected by means of a spring to an inelastic support. The static deflection due to the weight of the mass is 60 mm. The support is oscillated with simple harmonic motion at 3Hz and amplitude 10.0mm. Determine the amplitude of vibration of the mass and phase angle if the damping is negligible.

The mass is now damped in an oil bath which exerts a resistance proportional to velocity, and the spring anchorage is oscillated as before. It is observed that the amplitude of vibration of the mass is now one-half of its previous value. Find the damping ratio, and the phase between the motions of the mass and support.

Solutions

Expert Solution


Related Solutions

1.) A mass-spring system consists of an object of mass 1 Kilogram connected to a spring...
1.) A mass-spring system consists of an object of mass 1 Kilogram connected to a spring with a stiffness of 9. The damping constant is 6. Derive the function (1) that determines the distance from the equilibrium point if the initial position is 3 meters from the equilibrium point and the initial speed is 3 meters per second. a.) What is the maximum distance from the equilibrium point? b.) Determine the general solution of the nonhomogeneous linear differential equation using...
Design a straight ended helical torsion spring for a static load 200 N-m at a deflection...
Design a straight ended helical torsion spring for a static load 200 N-m at a deflection of 45 deg with a safety factor of 1.8. Specify all parameters necessart to manufacture the spring state all assumntions. You make the following design choices: *Use unpeened oil tempered wire with 40mm long, straight ends. The coil is loaded to close it * Design safety factory Nyd=1.8 *spring index C=11 *Yield Strength Factor K=0.85 *length of the ends L1=40 mm=L2 *Material choice =...
a) A block with a mass of 0.600 kg is connected to a spring, displaced in...
a) A block with a mass of 0.600 kg is connected to a spring, displaced in the positive direction a distance of 50.0 cm from equilibrium, and released from rest at t = 0. The block then oscillates without friction on a horizontal surface. After being released, the first time the block is a distance of 20.0 cm from equilibrium is at t = 0.200 s. What is the block's period of oscillation? b) A block with a mass of...
A block of mass 1.59 kg is connected to a spring of spring constant 148 N/m...
A block of mass 1.59 kg is connected to a spring of spring constant 148 N/m which is then set into oscillation on a surface with a small coefficient of kinetic friction. The mass is pulled back 30.6 cm to the right and released. On the first right to left oscillation, the mass reaches 29.38 cm to the left. Part A What is the coefficient of friction? Part B To what distance does the mass return on the slide back...
A seismic instrument (a mass connected to a spring and a damper) is employed to record...
A seismic instrument (a mass connected to a spring and a damper) is employed to record a periodic input signal y(t)=0.5cos(15?t), where y = displacement [cm], t = time [sec]. The damping ratio of the instrument is 0.6. Select a combination of mass, spring constant, and damping coefficient to yield less than a 5% amplitude error in measuring the input signal.
A block with mass M is connected to one end of a horizontal spring of constant...
A block with mass M is connected to one end of a horizontal spring of constant k, the other end of which is attached to the wall. The block moves with a simple harmonic motion on a frictionless surface. The amplitude of the harmonic motion is A1. When the block passes through the equilibrium position, a piece of plasticine, of mass m, is dropped vertically on the block and remains glued to it. Calculate the energy of the system in...
A spring with a spring rate of 75 lb/in has a working deflection of 1 in....
A spring with a spring rate of 75 lb/in has a working deflection of 1 in. It provides a minimum of 150 lb at installation. The spring is formed from 0.25 in diameter unpeened music wire. The coil has squared and ground ends, and it fits in a 2.1 in diameter hole with 0.1 in clearance. Assuming a 15% clash allowance, find: a) Safety factor for infinite life in fatigue b) Shut height c) Safety factor at shut height d)...
A block of wood of mass 4 kg is connected to a spring, whose other end...
A block of wood of mass 4 kg is connected to a spring, whose other end is tethered to a wall. As the spring is stretched and compressed, the block undergoes simple harmonic motion on the (frictionless) floor. The displacement of the block with respect to its equilibrium position is x = 0.205 cos ( 22.5 t ) where x is measured in m and t is measured in seconds. 1.) Which of these statements is true at time t...
A 3.9 kg mass is connected to a spring (k=179 N/m) and is sliding on a...
A 3.9 kg mass is connected to a spring (k=179 N/m) and is sliding on a horizontal frictionless surface. The mass is given an initial displacement of +18 cm and released with an initial velocity of -16 cm/s. Determine the acceleration of the spring at t=1.9 seconds. (include units with answer)
1. A 50-cm-long spring is suspended from the ceiling. A 230g mass is connected to the...
1. A 50-cm-long spring is suspended from the ceiling. A 230g mass is connected to the end and held at rest with the spring unstretched. The mass is released and falls, stretching the spring by 18cm before coming to rest at its lowest point. It then continues to oscillate vertically. a. What is the spring constant? (K=) b. What is the amplitude of the oscillation? c. What is the frequency of the oscillation? 2. Suppose the free-fall accelaration at some...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT