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Problem 5: A block weighing 40.0 N is suspended from a spring that has a force...
Problem 5: A block weighing 40.0 N is suspended from a spring that has a force constant of 200 N/m. The system is undamped (b 0) and is subjected to a harmonic driving force of frequency 10.0 Hz, resulting in a forced-motion amplitude of 2.00 cm. (a) Determine the maximum value of the driving force. The same system of block and spring are now moving in a fluid with damping coefficient b25 kg/s. The system is driven by an external...
A mass of 10 kg is suspended by a spring having a stiffness of 10000o N/m....
A mass of 10 kg is suspended by a spring having a stiffness of 10000o N/m. The viscous damping causes the amplitude to decrease to one-tenth of the initial value in four complete oscillations. If a periodic force of 150 cos 50t is applied to the mass in vertical direction, (a) Find the amplitude of the forced vibration (b) What is its amplitude at resonance? (c) Comment on the results obtained in part (a) and (b) (15 markah/marks)
Consider a single degree of freedom (SDOF) with mass-spring-damper system
Consider a single degree of freedom (SDOF) with mass-spring-damper system subjected to harmonic excitation having the following characteristics: Mass, m = 850 kg; stiffness, k = 80 kN/m; damping constant, c = 2000 N.s/m, forcing function amplitude, f0 = 5 N; forcing frequency, ωt = 30 rad/s. (a) Calculate the steady-state response of the system and state whether the system is underdamped, critically damped, or overdamped. (b) What happen to the steady-state response when the damping is increased to 18000 N.s/m? (Hint: Determine...
A spring-mass system with m = 8 kg and k = 4000 N/m subjected to a...
A spring-mass system with m = 8 kg and k = 4000 N/m subjected to a harmonic force of amplitude 200 N and frequency (). When the mass of the system is increased by 20% from its original value, the amplitude of the forced motion of the new mass is observed to be 25% off the original one. Determine the frequency of the harmonic force and the amplitude of original system
A reciprocating pump weighing W-150 lb, is mounted at a middle of a steel plate of thickness 0.5 ...
A reciprocating pump weighing W-150 lb, is mounted at a middle of a steel plate of thickness 0.5 in., width of 20 in., and clamped along two edges as shown. During operation of pump, the plate is subjected to a harmonic force F(t)-P, . cos(ω·) [lb] 0.5 in. 100 in. where the amplitude of harmonic force is Fo=50 lb and its angular frequency: ω-62832 radl s Model the system as a simple spring and mass system in the horizontal plane....
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)
A 10 kg object is suspended from a spring causes the spring to lengthen by 5...
A 10 kg object is suspended from a spring causes the spring to lengthen by 5 cm down. The object is subjected to a force of 2cos (t / 4) N (newtons), and it moves in an environment where the viscosity force is 1N when the speed is 6 cm / s. If the object is set in motion from its position of equilibrium with an initial speed of 2 cm / s, formulate the initial value problem that describes...
A 10 kg object is suspended from a spring causes the spring to lengthen by 5...
A 10 kg object is suspended from a spring causes the spring to lengthen by 5 cm down. The object is subjected to a force of 2cos (t / 4) N (newtons), and it moves in a medium where the viscosity force is 1N when the speed is 6 cm / s. If the object is set in motion from its position of equilibrium with an initial speed of 2 cm / s, formulate the initial value problem that describes...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a s...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mx+cx + kx = A sin(at) 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 5 and the un-damped natural frequency Using the given formulas for...
Problem 42P: Chapter: CH9 - Problem: 42P At time t = 0, a forced harmonic oscillator...
Problem 42P: Chapter: CH9 - Problem: 42P At time t = 0, a forced harmonic oscillator occupies position (0) = 0.1 mand has a velocity x(0) 0. The mass of the oscillator is m = 10 kg, and the stiffness of the spring is k-1000 N/m. Calculate the motion of the system if the forcing function is AO - FO sin wor, with F0 - 10 N and wo - 200 rad/s. An off-highway truck drives onto a concrete deck...
Problem 5: A block weighing 40.0 N is suspended from a spring that has a force constant of 200 N/m. The system is undamped (b 0) and is subjected to a harmonic driving force of frequency 10.0 Hz, resulting in a forced-motion amplitude of 2.00 cm. (a) Determine the maximum value of the driving force. The same system of block and spring are now moving in a fluid with damping coefficient b25 kg/s. The system is driven by an external...
A mass of 10 kg is suspended by a spring having a stiffness of 10000o N/m. The viscous damping causes the amplitude to decrease to one-tenth of the initial value in four complete oscillations. If a periodic force of 150 cos 50t is applied to the mass in vertical direction, (a) Find the amplitude of the forced vibration (b) What is its amplitude at resonance? (c) Comment on the results obtained in part (a) and (b) (15 markah/marks)
A reciprocating pump weighing W-150 lb, is mounted at a middle of a steel plate of thickness 0.5 in., width of 20 in., and clamped along two edges as shown. During operation of pump, the plate is subjected to a harmonic force F(t)-P, . cos(ω·) [lb] 0.5 in. 100 in. where the amplitude of harmonic force is Fo=50 lb and its angular frequency: ω-62832 radl s Model the system as a simple spring and mass system in the horizontal plane....
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)
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mx+cx + kx = A sin(at) 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 5 and the un-damped natural frequency Using the given formulas for...
Problem 42P: Chapter: CH9 - Problem: 42P At time t = 0, a forced harmonic oscillator occupies position (0) = 0.1 mand has a velocity x(0) 0. The mass of the oscillator is m = 10 kg, and the stiffness of the spring is k-1000 N/m. Calculate the motion of the system if the forcing function is AO - FO sin wor, with F0 - 10 N and wo - 200 rad/s. An off-highway truck drives onto a concrete deck...
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