A spring is stretched 6 m by a mass that weighs 8 kg. The mass is...
A spring is stretched 6 m by a mass that weighs 8 kg. The mass is attached to a dashpot mechanism that has a damping constant of 0.25 Ns/m, and is acted on by an external force of 4 cos(2t) N.
(a) Write down the IVP that describes the system.
(b) Determine the steady-state response of this system (you may simply use the formula in the text and plug in the appropriate numerical coefficients). Note: You do not need to find the phase shift.
(c) If the given mass is replaced by a mass m, determine the value of m for which the amplitude of the steady-state response is maximum. Give an exact (not decimal) answer.
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A spring is stretched 6 m by a mass that weighs 8 kg. The mass
is...
A spring is stretched by 9 in by a mass weighing 15 lb. The mass is...
A spring is stretched by 9 in by a mass weighing 15 lb. The mass is attached to a dashpot mechanism that has a damping constant 0.35 lb-s/ft and is acted on by an external force of 9 cos(6t) lb. Determine the steady state response of this system. Use 32 ft/s² as the acceleration due to gravity. Pay close attention to the units. U(t) = ft
Frequency Response of a mass-spring-dashpot system Consider a mass-spring-dashpot system driven b...
Use matlab for the following:
Frequency Response of a mass-spring-dashpot system Consider a mass-spring-dashpot system driven by a unit amplitude harmonic input mdx/dt+ cdx/dt + kx- Sin (wt) Use Matlab to simulate time response for ten well-chosen values of w for 3 different values of dimensionless damping factor : 0, between 0 and 1, larger than 1. Record and plot the steady state values of amplitude.
Frequency Response of a mass-spring-dashpot system Consider a mass-spring-dashpot system driven by a unit...
please find amplitude and freq of the steady state solution An 8-kg mass is attached to...
please find amplitude and freq
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An 8-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 4 sin 2t cos 2t is applied to the system. Determine the amplitude and frequency of the steady-state solution.
A 0.500 kg mass is attached to a spring of constant 150 N/m. A driving force...
A 0.500 kg mass is attached to a spring of constant 150 N/m. A driving force F(t) = ( 12.0N) cos(ϝt) is applied to the mass, and the damping coefficient b is 6.00 Ns/m. What is the amplitude (in cm) of the steady-state motion if ϝ is equal to half of the natural frequency ϝ0 of the system?
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system...
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system is acted upon by a force modelled as a harmonic force: F(t) = 0.2 sin(wt) Force is given in N and time in seconds. W Figure 31.1 Nos Given numerical values: m = 10 kg C=5 M k = 1000 = 1) draw the correct Free-Body-Diagram and determine the equation of motion [2 marks) 2) determine the natural frequency and the damping ratio of...
A mass-spring-damper system is shown below. If a periodic external forceAssume: r acts on the mass...
A mass-spring-damper system is shown below. If a periodic external forceAssume: r acts on the mass as graphed below, what is the steady state response of the system? D= Spring Mass m External force r(t) Dashpot Vibrating system under considerati r(t) ?/2
A mass weighing 4 kg stretches a spring by 6 centimeters. The damping constant is c-0.8 External ...
A mass weighing 4 kg stretches a spring by 6 centimeters. The damping constant is c-0.8 External vibrations create a force of FO 8 sin(50) kg. Find the steady-state solution and identify its amplitude and phase shift. 2,048 2,496 ゲー2.sas cos(5) + 2,545 sin(5) ゲー2.545 ゲisas cos(5) + 2.545 sin(5) ゲ2.545 2.048 cos(50- 2.545 2,496 2,545 sin(50 2,048 2,545 2,496 2.048 cos50- 2.545 2,545 A series circuit has an inductor of 1 henry, a resistor of 10 ohms and a...
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
A mass weighing 4 kg stretches a spring by 6 centimeters. The damping constant is c 0.S. External...
is option 1 correct answer?
A mass weighing 4 kg stretches a spring by 6 centimeters. The damping constant is c 0.S. External vibrations create a force of F(t) 2 sin(3t) kg. Find the steady-state solution and identify it:s amplitude and phase shift pS4,.841 84.84122000 84,841 sin(31) 84.8422000 1.680 cos) S4S41 8484 sin(3) 22.000 sin30) p S4,S41 cos(3t 1.680 cos) S4,841 22.000 sin(3t) pS4,.841
A mass weighing 4 kg stretches a spring by 6 centimeters. The damping constant is c...
A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is...
A spring-mass system has a
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resistance numerically equal to the magnitude of the instantaneous
velocity. If the system is driven by an external force of (27 cos
3t − 18 sin 3t) N, determine the steady state response. Express
your answer in the form R cos(ωt − δ). (Let u(t) be the
displacement...
A spring is stretched by 9 in by a mass weighing 15 lb. The mass is attached to a dashpot mechanism that has a damping constant 0.35 lb-s/ft and is acted on by an external force of 9 cos(6t) lb. Determine the steady state response of this system. Use 32 ft/s² as the acceleration due to gravity. Pay close attention to the units. U(t) = ft
Use matlab for the following:
Frequency Response of a mass-spring-dashpot system Consider a mass-spring-dashpot system driven by a unit amplitude harmonic input mdx/dt+ cdx/dt + kx- Sin (wt) Use Matlab to simulate time response for ten well-chosen values of w for 3 different values of dimensionless damping factor : 0, between 0 and 1, larger than 1. Record and plot the steady state values of amplitude.
Frequency Response of a mass-spring-dashpot system Consider a mass-spring-dashpot system driven by a unit...
please find amplitude and freq
of the steady state solution
An 8-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 4 sin 2t cos 2t is applied to the system. Determine the amplitude and frequency of the steady-state solution.
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system is acted upon by a force modelled as a harmonic force: F(t) = 0.2 sin(wt) Force is given in N and time in seconds. W Figure 31.1 Nos Given numerical values: m = 10 kg C=5 M k = 1000 = 1) draw the correct Free-Body-Diagram and determine the equation of motion [2 marks) 2) determine the natural frequency and the damping ratio of...
A mass-spring-damper system is shown below. If a periodic external forceAssume: r acts on the mass as graphed below, what is the steady state response of the system? D= Spring Mass m External force r(t) Dashpot Vibrating system under considerati r(t) ?/2
A mass weighing 4 kg stretches a spring by 6 centimeters. The damping constant is c-0.8 External vibrations create a force of FO 8 sin(50) kg. Find the steady-state solution and identify its amplitude and phase shift. 2,048 2,496 ゲー2.sas cos(5) + 2,545 sin(5) ゲー2.545 ゲisas cos(5) + 2.545 sin(5) ゲ2.545 2.048 cos(50- 2.545 2,496 2,545 sin(50 2,048 2,545 2,496 2.048 cos50- 2.545 2,545 A series circuit has an inductor of 1 henry, a resistor of 10 ohms and a...
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
is option 1 correct answer?
A mass weighing 4 kg stretches a spring by 6 centimeters. The damping constant is c 0.S. External vibrations create a force of F(t) 2 sin(3t) kg. Find the steady-state solution and identify it:s amplitude and phase shift pS4,.841 84.84122000 84,841 sin(31) 84.8422000 1.680 cos) S4S41 8484 sin(3) 22.000 sin30) p S4,S41 cos(3t 1.680 cos) S4,841 22.000 sin(3t) pS4,.841
A mass weighing 4 kg stretches a spring by 6 centimeters. The damping constant is c...
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spring constant of 3 N/m. A mass of 2 kg is attached to the spring,
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resistance numerically equal to the magnitude of the instantaneous
velocity. If the system is driven by an external force of (27 cos
3t − 18 sin 3t) N, determine the steady state response. Express
your answer in the form R cos(ωt − δ). (Let u(t) be the
displacement...
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