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1. An undamped mass on a spring system vibrates freely after being perturbed from an initial...
(Undamped system) An iron ball of mass 10kg is attached to a spring having a spring...
(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.
4. (30%) Consider the following system that consists of a mass m-10kg, coil spring of stiffness...
4. (30%) Consider the following system that consists of a mass m-10kg, coil spring of stiffness k-1000N/m, and damping c-200Ns/m. 1) Suppose that the mass is initially at rest and is given an initial velocity of 3 m/s Find the free vibration response of the mass. 2) Suppose that at a later time, a harmonic force F (t)- sin15t is acted on the mass. Determine the amplitude of the forced vibration response. F, sin
EXam 2 Name: 1. A n undamped vertical system consists of a mass weighing 100 N...
EXam 2 Name: 1. A n undamped vertical system consists of a mass weighing 100 N and a spring of stiffness 5000 N/m. It is acted on by a harmonic force of amplitude 80 N and frequency 5 Hz. Find i) The displacement of the spring due to the weight of the mass, The static displacement of the spring due to the maximum applied force, and The amplitude of forced motion of the mass for zero initial conditions iii)
Problem 2. Recall that any undamped spring-mass system is described by an initial value problem of...
Problem 2. Recall that any undamped spring-mass system is described by an initial value problem of the form m" + ky= 0, (0) = 0, v(0) = to, where m is the mass and k is the spring constant. Since there is no damping, we would expect that no energy is lost as the mass moves. That is, the total energy (potential plus kinetic) in the system at any time I should equal the initial amount of energy in the...
1. DETAILS ZILLDIFFEQMODAP11 5.R.011. MY NOTES ASK YOUR TEACHER A free undamped spring/mass system oscillates with...
1. DETAILS ZILLDIFFEQMODAP11 5.R.011. MY NOTES ASK YOUR TEACHER A free undamped spring/mass system oscillates with a period of 3 seconds. When 12 pounds are removed from the spring, the system then has a period of 2 seconds. What was the weight of the original mass on the spring? (Round your answer to one decimal place.) Ib
help me with this Consider the vibration of mass spring system given by the initial value...
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Consider the vibration of mass spring system given by the initial value problem m d²x dt2 dx +b. dt + kx = 0 x(0)=0, x'(0) = 1 Where m, b, k are nonnegative constants and b2 < 4mk. Show that a solution to the problem is given by b2 2m e 2m sin 4mk-b2 4mk 2m t (CO2:P01 - 8 Marks) b. A 200 g mass stretches a spring 5 cm. If it is release from...
If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant...
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
QUESTION 2 (20 MARKS) a Consider the vibration of mass spring system given by the initial...
QUESTION 2 (20 MARKS) a Consider the vibration of mass spring system given by the initial value problem dx dx de+b + kx = 0 dt *(0) = 0 . x'(0) = 1 Where m, b, k are nonnegative constants and b2 < 4mk. Show that a solution to the problem is given by X(t) = 2m Amk- em sin 4mk-02 2m (CO2:P01 - 8 Marks) b. A 200 g mass stretches a spring 5 cm. If it is release...
2. An undamped mass on a spring has a natural frequency of 10Hz. The system consists...
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]
The system parameters of a freely-vibrating damped SDOF system are as follows: Mass, m= 100 kg...
The system parameters of a freely-vibrating damped SDOF system are as follows: Mass, m= 100 kg Damping Factor, c = 200 kg/s Spring Stiffness, k = 3000 N/m Initial Position, x, = 1 m Initial Velocity, v,= 0 m/s a) Create a MATLAB code and using the specified system parameters compute (using the correct units) the system characteristics: 1) natural (circular) frequency on; 2) cyclic frequency fn; 3) cyclic period p; 4) damped natural (circular) frequency 0g, and 5) damping...
4. (30%) Consider the following system that consists of a mass m-10kg, coil spring of stiffness k-1000N/m, and damping c-200Ns/m. 1) Suppose that the mass is initially at rest and is given an initial velocity of 3 m/s Find the free vibration response of the mass. 2) Suppose that at a later time, a harmonic force F (t)- sin15t is acted on the mass. Determine the amplitude of the forced vibration response. F, sin
EXam 2 Name: 1. A n undamped vertical system consists of a mass weighing 100 N and a spring of stiffness 5000 N/m. It is acted on by a harmonic force of amplitude 80 N and frequency 5 Hz. Find i) The displacement of the spring due to the weight of the mass, The static displacement of the spring due to the maximum applied force, and The amplitude of forced motion of the mass for zero initial conditions iii)
Problem 2. Recall that any undamped spring-mass system is described by an initial value problem of the form m" + ky= 0, (0) = 0, v(0) = to, where m is the mass and k is the spring constant. Since there is no damping, we would expect that no energy is lost as the mass moves. That is, the total energy (potential plus kinetic) in the system at any time I should equal the initial amount of energy in the...
1. DETAILS ZILLDIFFEQMODAP11 5.R.011. MY NOTES ASK YOUR TEACHER A free undamped spring/mass system oscillates with a period of 3 seconds. When 12 pounds are removed from the spring, the system then has a period of 2 seconds. What was the weight of the original mass on the spring? (Round your answer to one decimal place.) Ib
help me with this
Consider the vibration of mass spring system given by the initial value problem m d²x dt2 dx +b. dt + kx = 0 x(0)=0, x'(0) = 1 Where m, b, k are nonnegative constants and b2 < 4mk. Show that a solution to the problem is given by b2 2m e 2m sin 4mk-b2 4mk 2m t (CO2:P01 - 8 Marks) b. A 200 g mass stretches a spring 5 cm. If it is release from...
QUESTION 2 (20 MARKS) a Consider the vibration of mass spring system given by the initial value problem dx dx de+b + kx = 0 dt *(0) = 0 . x'(0) = 1 Where m, b, k are nonnegative constants and b2 < 4mk. Show that a solution to the problem is given by X(t) = 2m Amk- em sin 4mk-02 2m (CO2:P01 - 8 Marks) b. A 200 g mass stretches a spring 5 cm. If it is release...
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]
The system parameters of a freely-vibrating damped SDOF system are as follows: Mass, m= 100 kg Damping Factor, c = 200 kg/s Spring Stiffness, k = 3000 N/m Initial Position, x, = 1 m Initial Velocity, v,= 0 m/s a) Create a MATLAB code and using the specified system parameters compute (using the correct units) the system characteristics: 1) natural (circular) frequency on; 2) cyclic frequency fn; 3) cyclic period p; 4) damped natural (circular) frequency 0g, and 5) damping...
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