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A) Use judicious guessing to solve the nonhomogeneous spring-mass model with m g(t)4cos(5t) 10,-2...
Item 13 This question is about the homogeneous spring-mass model mj + y+ky 0. (a) Let...
Item 13 This question is about the homogeneous spring-mass model mj + y+ky 0. (a) Let m 10, u37, and k= 30. Which case is this, and how do you know? (By "which case is this," I mean, "Is the system undamped, underdamped, critically damped, or overdamped?") (b) Suppose m 10, 0, and k30. Which case is this, and how do you know? (c) Suppose now that m 10, 20, and k30. Which case is this, and how do you...
A mass m = 3 kg is attached to a spring with spring constant k =...
A mass m = 3 kg is attached to a spring with spring constant k = 3 N/m and oscillates with simple harmonic motion along the x-axis with an amplitude A = 0.10 m. (a) What is the angular frequency of this oscillation? (b) What is the period T and the frequency f of the oscillation? (c) If the phase constant = 0, write down expressions for the displacement, velocity and acceleration of the mass as a function...
Part 2: (Theory) Simple Harmonie Motion in a Mass-Spring System Sketch a simple horizontal, mass-spring system...
Part 2: (Theory) Simple Harmonie Motion in a Mass-Spring System Sketch a simple horizontal, mass-spring system with the mass displaced slightly from its equilibrium position (x=0). Draw the forces acting on the mass (you should have three; neglect friction). Now imagine that the system is released from rest. According to Newton's Second Law, F=ma, the equation of motion for the mass can be written as: (1) m dr 1. By direct substitution, show explicitly that x(t) - Acos(wt + )...
F(t) 1. The spring-mass system shown in the figure has • m=40kg, • k = 38.6kN...
F(t) 1. The spring-mass system shown in the figure has • m=40kg, • k = 38.6kN / m • C=0.2518kNs / m The mass vibrates harmonically with an amplitude of 1mm and angular frequency @=100rad /s . 1.1 What is the amplitude of the force? 1.2 What is the frequency of the force that yields the maximum vibration amplitude? If the force amplitude is the same as the value computed in 1.1, what is the resulting vibration amplitude?
Question (b) Ans : root(7/2) , 16/((5)^(1/2)) 9. Consider a mass-spring system as shown in the...
Question (b)
Ans : root(7/2) , 16/((5)^(1/2))
9. Consider a mass-spring system as shown in the figure with a body of mass m, a spring and a dashpot. Let k, c and r(t) be the spring constant, the damping constant and driving force, respectively Let y(t) be the displacementMass of the body from the equilibrium with downward direction as positive. b) [7pts] Let m=1, c=1, k=4, and r(t) 8cosut. Determine w such that you get the steady-state vibration of maximum...
Suppose a mass of 1 kg is attached to a spring with spring constant k =...
Suppose a mass of 1 kg is attached to a spring with spring constant k = 2, and rests at equilibrium position. Starting at t = 0, an external force of f(t) = e t is applied to the system. Suppose the surrounding medium offers a damping force numerically equal to β times the instantaneous velocity, where β > 0 is some given number. (a) What is the IVP governing this harmonic motion. (b) For what value(s) of β will...
QUESTION 10 When a 200 g mass attached to a horizontal spring (k= 25 N/m) is...
QUESTION 10 When a 200 g mass attached to a horizontal spring (k= 25 N/m) is pushed 10 cm into the spring and released, it undergoes simple harmonic motion. Find the quantities below for this oscillating system: (a) The angular frequency (rad/sec) QUESTION 11 When a 200 g mass attached to a horizontal spring (k-25 N/m) is pushed 10 cm into the spring and released, it undergoes simple harmonic motion. Find the quantities below for this oscillating system. (b) Th...
For a mass-spring oscillator, Newton's second law implies that the position y(t) of the mass is...
For a mass-spring oscillator, Newton's second law implies that the position y(t) of the mass is governed by the second-order differential equation my'' (t) + by' (t) + ky(t) = 0. (a) Find the equation of motion for the vibrating spring with damping if m= 10 kg, b = 100 kg/sec, k = 260 kg/sec?. y(0) = 0.3 m, and y'(0) = -0.4 m/sec. (b) After how many seconds will the mass in part (a) first cross the equilibrium point?...
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?...
Consider a damped forced mass-spring system with m = 1, γ = 2, and k =...
Consider a damped forced mass-spring system with m = 1, γ = 2, and k = 26 under the influence of an external force F(t) = 82 cos(ωt). We can prove that the amplitude of this motion is given by R(ω) = p F0 m2 (ω0 2 − ω2 ) 2 + γ 2ω2 = 82 √ ω4 − 48ω2 + 76 For what value of ω will the maximum amplitude occur? When resonance will occur and how would you...
Item 13 This question is about the homogeneous spring-mass model mj + y+ky 0. (a) Let m 10, u37, and k= 30. Which case is this, and how do you know? (By "which case is this," I mean, "Is the system undamped, underdamped, critically damped, or overdamped?") (b) Suppose m 10, 0, and k30. Which case is this, and how do you know? (c) Suppose now that m 10, 20, and k30. Which case is this, and how do you...
Part 2: (Theory) Simple Harmonie Motion in a Mass-Spring System Sketch a simple horizontal, mass-spring system with the mass displaced slightly from its equilibrium position (x=0). Draw the forces acting on the mass (you should have three; neglect friction). Now imagine that the system is released from rest. According to Newton's Second Law, F=ma, the equation of motion for the mass can be written as: (1) m dr 1. By direct substitution, show explicitly that x(t) - Acos(wt + )...
F(t) 1. The spring-mass system shown in the figure has • m=40kg, • k = 38.6kN / m • C=0.2518kNs / m The mass vibrates harmonically with an amplitude of 1mm and angular frequency @=100rad /s . 1.1 What is the amplitude of the force? 1.2 What is the frequency of the force that yields the maximum vibration amplitude? If the force amplitude is the same as the value computed in 1.1, what is the resulting vibration amplitude?
Question (b)
Ans : root(7/2) , 16/((5)^(1/2))
9. Consider a mass-spring system as shown in the figure with a body of mass m, a spring and a dashpot. Let k, c and r(t) be the spring constant, the damping constant and driving force, respectively Let y(t) be the displacementMass of the body from the equilibrium with downward direction as positive. b) [7pts] Let m=1, c=1, k=4, and r(t) 8cosut. Determine w such that you get the steady-state vibration of maximum...
QUESTION 10 When a 200 g mass attached to a horizontal spring (k= 25 N/m) is pushed 10 cm into the spring and released, it undergoes simple harmonic motion. Find the quantities below for this oscillating system: (a) The angular frequency (rad/sec) QUESTION 11 When a 200 g mass attached to a horizontal spring (k-25 N/m) is pushed 10 cm into the spring and released, it undergoes simple harmonic motion. Find the quantities below for this oscillating system. (b) Th...
For a mass-spring oscillator, Newton's second law implies that the position y(t) of the mass is governed by the second-order differential equation my'' (t) + by' (t) + ky(t) = 0. (a) Find the equation of motion for the vibrating spring with damping if m= 10 kg, b = 100 kg/sec, k = 260 kg/sec?. y(0) = 0.3 m, and y'(0) = -0.4 m/sec. (b) After how many seconds will the mass in part (a) first cross the equilibrium point?...
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?...
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