Answered: 1 A-kg mass is attached to a spring… | bartleby

Related questions

Question

100%

1
A-kg mass is attached to a spring with stiffness 40 N/m. The damping constant for the system is 4 N-sec/m. If the mass is moved
m to the left of equilibrium and
15
given an initial leftward velocity of
14
m/sec, determine the equation of motion of the mass and give its damping factor, quasiperiod, and quasifrequency.

Expert Solution

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

A force of 5 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 1.2 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. x(t) = (b) Express the equation of motion in the form x(t) x(t) ft = ft = Ae¯^t sin(√√ ² - ^²t + 4) 9), which is given in (23) of Section 3.8. (Round p to two decimal places.) (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.) S
A SDOF has undamped natural frequency of 7 rad/sec. and a damping factor of 10%. The initial conditions are x0 = 0 and V0 = 0.5 m/sec. Find damped frequency and equation of motion of the system
A 1-kg mass is attached to a spring with stiffness 100 N/m. The damping constant for the system is 0.2 N-sec/m. If the mass is pushed rightward from the equilibrium position with a velocity of 1 m/sec, when will it attain its maximum displacement to the right?
A child with mass of 10 kg gets into a toy car with mass of 65 kg on a playground, causing it to sink on its spring (withspring constant 327 N/m). An adult walks by and gives the top of the car a shove, causing it to undergo oscillationswith amplitude 30 cm in the vertical direction. Assuming the oscillations are simple harmonic, what is the angularfrequency of the oscillations?ω = (in rad/s) a. 0.673 b. 1.715 c. 2.088 d. 2.243 e. 5.717
An 4-kg mass is attached to a spring hanging from the ceiling and allowed to come to rest. Assume that the spring constant is 20 N/m and the damping constant is 2 N-sec/m. At time t = 0, an external force of F(t) = 2 cos (2t + ) is applied to the system. Formulate the initial value problem describing the motion of the mass and determine the amplitude and period of the steady-state solution. Let y(t) to denote the displacement, in meters, of the mass from its equilibrium position. Set up a differential equation that describes this system. (give your answer in terms of y, y', y"). The amplitude of the steady-state solution is m. The period of the steady-state solution is radians. If you don't get this in 3 tries, you can get a hint.
A force of 9 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 1.2 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. ft x(t) = = -λt (b) Express the equation of motion in the form x(t) = Ae¯ sin(√²-2²t+ x(t) = = ft q²t + 9), which is given in (23) of Section 3.8. (Round p to two decimal places.) (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.) S
A 5.00 kg bob is connected to the ceiling via a light string, while an 8.50 kg uniform rod is also connected to the ceiling at one of its ends. Both objects are capable of oscillating in simple harmonic motion and share the same length, which is 2.25 m. Calculate the oscillation period for each pendulum under small displacements? If the mass of the bob is doubled, will there be any change in the period of the oscillations? Moreover, if the mass of the rod is quadrupled, will there be any alteration in the period of the oscillations? To ensure that both pendulums swing with an identical period while maintaining the length of the rod, what should be the new length of the string connected to the bob?
A ball whose mass is 1.7 kg is suspended from a spring whose stiffness is 6.5 N/m. The ball oscillates up and down with an amplitude of 11 cm. Suppose this apparatus were taken to the Moon, where the strength of the gravitational field is only 1/6 of that on Earth. What would the period be on the Moon?
a particle of mass m makes simple harmonic motion with force constant k around the equilibrium position x = 0. Calculate the valu of the amplitude and the phase constant if the initial conditions are x(0) = 0 and v(0) = -Vi (vi > 0). Draw x-t, v - t and a - t figures for one complete cycle of oscillations.
A simple harmonic motion of a point mass m can be expressed byx = 0.25sin(4pt +p/6) m ( time t in ses). a)Find the amplitude for the oscillation in m. b)Find the frequency of the oscillation (in Hz). c)Find the maximum speed for the oscillation (in m/s d)Find the maximum acceleration for the oscillation (in m/s2 ) e)Find the initial position of the mass m (in m) f)Find the total energy for the oscillation (in Jules)
A 2-kg mass is attached to a spring hanging from the ceiling, thereby causing the spring to stretch 1.4 m upon coming to rest at equilibrium. At time t= 0, an external force of F(t) = cos 2t N is applied to the system. The damping constant for the system is 4 N-sec/m. Determine the steady-state solution for the system. The steady-state solution is y(t)=- plz help
A 3-kg mass is attached to a spring with stiffness 60 N/m. The damping constant for the system is 12√5 N-sec/m. If the mass is pulled 20 cm to the right of equilibrium and given an initial rightward velocity of 4 m/sec, what is the maximum displacement from equilibrium that it will attain?

SEE MORE QUESTIONS