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13. A damped mass-spring system with mass m, spring constant k, and damping constant b is...
A damped oscillator with natural frequency wo and damping K is driven by a period square...
A damped oscillator with natural frequency wo and damping K is driven by a period square wave force with amplitude A such that F(t)= A Find the Fourier series for F(t), and solve for the amplitude of the motion of the oscillator. For which frequency wn is the resonance condition the most closely satisfied? Plot the maximum amplitude (in units of A) as a function of wn for the conditions with the spring constant k 1, m 2, K 0.1,...
1. The exponential damping factor K of a spring is 1/10 the critical value. The spring...
1. The exponential damping factor K of a spring is 1/10 the critical value. The spring has an undamped frequency of wo. A mass m is attached to the spring. Find a) The resonant frequency in terms of w. (3 marks) b) The quality factor (1 mark) c) The phase angle when the spring is driven by a force F. at a driving frequency (1 marks) d) The steady-state amplitude of oscillation when it is driven at this frequency in...
A damped vibrating system consists of a spring of stiffness k = 3,600 N/m and a...
A damped vibrating system consists of a spring of stiffness k = 3,600 N/m and a mass of 5 kg. It is damped so that each amplitude is 99% of the previous one (i.e. after a full cycle). (a) Find the frequency of oscillation. (b) Find the damping constant. (c) Find the amplitude of the force of resonant frequency necessary to to keep the system vibrating at 25mm amplitude. (d) What is the rate of increase in amplitude if, at...
3.4. A harmonic oscillator with mass m, natural angular frequency wo, and damping constant r is...
3.4. A harmonic oscillator with mass m, natural angular frequency wo, and damping constant r is driven by an external force FCt) Fo cos(wot)N. W show that xp A sin(wot) is a solution if A Fo/rwo. rite the equation of motion and use it to
A car and its suspension system act as a block of mass m= on a vertical spring with k 1.2 x 10 N m, which is damped...
A car and its suspension system act as a block of mass m= on a vertical spring with k 1.2 x 10 N m, which is damped when moving in the vertical direction by a damping force Famp =-rý, where y is the 1200 kg sitting 4. (a) damping constant. If y is 90% of the critical value; what is the period of vertical oscillation of the car? () by what factor does the oscillation amplitude decrease within one period?...
Problem # 4 15 points The base of a damped spring-mass system, with m 25 kg...
Problem # 4 15 points The base of a damped spring-mass system, with m 25 kg and k 2500 N/m, is subjected to a harmonic excitation y(t) Xo cos ω. The amplitude of the mass is found to be 0.05 m when the base is excited at the natural frequency of the system with Yo 0.0 m. Determine the damping constant of the system.
A spring has a Damping resistance of c = 100, a mass of m = .1kg...
A spring has a Damping resistance of c = 100, a mass of m = .1kg and a spring constant value of k = 10 kg/ms2 . a) is this system under , over or critically damped? b) If underdamped, calculate the oscillation frequency of the spring.
A damped osillator has a mass (m = 2.00kg), a spring (k = 10.0N/m), and a...
A damped osillator has a mass (m = 2.00kg), a spring (k = 10.0N/m), and a damping coefficient b = 0.102kg/s. undamped angular frequency of the system is 2.24rad/s. If the initial amplitude is 0.250m, How many periods of motion are necessary for the amplitude to be reduced to 3/4 it initial value? is this system underdamped, critically damped, or overdamped
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 mi+ci +kx- Asin(ot) 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 un-damped natural frequency on a. and the
A second order mechanical system of a...
21.6 A,B,C,D result given in part c of this exercise. 21.6. Consider a damped mass/spring system...
21.6 A,B,C,D
result given in part c of this exercise. 21.6. Consider a damped mass/spring system given by m dy gdy tr dt + ky = Fo cos(nt) where m. y. K and Fo are all positive constants. (This is the same as equation (214) a. Using the method of educated guess, derive the particular solution given by equation ser (21.10) on page 409. genelaidi b. Then show that the solution in the previous part can be rewritten as described...
A damped oscillator with natural frequency wo and damping K is driven by a period square wave force with amplitude A such that F(t)= A Find the Fourier series for F(t), and solve for the amplitude of the motion of the oscillator. For which frequency wn is the resonance condition the most closely satisfied? Plot the maximum amplitude (in units of A) as a function of wn for the conditions with the spring constant k 1, m 2, K 0.1,...
1. The exponential damping factor K of a spring is 1/10 the critical value. The spring has an undamped frequency of wo. A mass m is attached to the spring. Find a) The resonant frequency in terms of w. (3 marks) b) The quality factor (1 mark) c) The phase angle when the spring is driven by a force F. at a driving frequency (1 marks) d) The steady-state amplitude of oscillation when it is driven at this frequency in...
A damped vibrating system consists of a spring of stiffness k = 3,600 N/m and a mass of 5 kg. It is damped so that each amplitude is 99% of the previous one (i.e. after a full cycle). (a) Find the frequency of oscillation. (b) Find the damping constant. (c) Find the amplitude of the force of resonant frequency necessary to to keep the system vibrating at 25mm amplitude. (d) What is the rate of increase in amplitude if, at...
3.4. A harmonic oscillator with mass m, natural angular frequency wo, and damping constant r is driven by an external force FCt) Fo cos(wot)N. W show that xp A sin(wot) is a solution if A Fo/rwo. rite the equation of motion and use it to
A car and its suspension system act as a block of mass m= on a vertical spring with k 1.2 x 10 N m, which is damped when moving in the vertical direction by a damping force Famp =-rý, where y is the 1200 kg sitting 4. (a) damping constant. If y is 90% of the critical value; what is the period of vertical oscillation of the car? () by what factor does the oscillation amplitude decrease within one period?...
Problem # 4 15 points The base of a damped spring-mass system, with m 25 kg and k 2500 N/m, is subjected to a harmonic excitation y(t) Xo cos ω. The amplitude of the mass is found to be 0.05 m when the base is excited at the natural frequency of the system with Yo 0.0 m. Determine the damping constant of the system.
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mi+ci +kx- Asin(ot) 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 un-damped natural frequency on a. and the
A second order mechanical system of a...
21.6 A,B,C,D
result given in part c of this exercise. 21.6. Consider a damped mass/spring system given by m dy gdy tr dt + ky = Fo cos(nt) where m. y. K and Fo are all positive constants. (This is the same as equation (214) a. Using the method of educated guess, derive the particular solution given by equation ser (21.10) on page 409. genelaidi b. Then show that the solution in the previous part can be rewritten as described...
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