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Using the Laplace transform method, find the function vt) if the system below is disturbed by...
find the general solution (y) using laplace transform (1 point) Consider a spring attached to a...
find the general solution (y) using laplace transform
(1 point) Consider a spring attached to a 1 kg mass, damping constant 8 = 5, and spring constant k = 6 The initial position of the spring is 4 metres beyond its resting length, and the initial velocity is -9 m/s. After 1 second, a constant force of 12 Newtons is applied to the system for exactly 2 seconds Set up a differential equation for the position of the spring y...
Question. Systems of ODEs of higher order can be solved by the Laplace transform method. As...
Question. Systems of ODEs of higher order can be solved by the Laplace transform method. As an important application, typical of many similar mechanical systems, consider coupled vibrating masses on springs. Wrovov The mechanical system in the Figure consists of two bodies of mass 1 on three springs of the same spring constant k and of negligibly small masses of the springs. Also damping is assumed to be practically zero. Then the model of the physical system is the system...
6) The 18 kg mass of a spring-mass system is initially at rest. At time =...
6) The 18 kg mass of a spring-mass system is initially at rest. At time = 0, a 400 N force is applied (toward the right). Spring constant is 100 kN / m, and the viscous damping coefficient is 520 Ns/m Determine the transient response F = (400 N) 1(t) Delay time [HINT: may need to a) graphing calculator, fixed point iteration; or calculator equation solver] b) c) use a m Peak time Maximum overshoot (in mm)
6) The 18...
A single dof vibration system, modeled by a mass of 50 kg, damping coefficient of 300...
A single dof vibration system, modeled by a mass of 50 kg, damping coefficient of 300 Ns/m, and spring constant of 5000 N/m, is subjected to periodic displacement excitation u(t) as shown in the figure below. 1. Derive the equation of motion 2. Using Laplace transform, find characteristic equation. 3. Find the undamped and damped natural frequencies. 4. Find the damping ratio. 5. Find the transfer function of output x(t) to the periodic input u(t) using Laplace transform.
Find the function of each graph u(x) and then u(t) and take the laplace transformation of u(t). Knowing that x=vt Profile one (step) 0.25 02 0.15 0.1 0.05 005 0.5 0.5 1.5 ength im) Profile two (r...
Find the function of each graph u(x) and then u(t) and take the
laplace transformation of u(t). Knowing that x=vt
Profile one (step) 0.25 02 0.15 0.1 0.05 005 0.5 0.5 1.5 ength im) Profile two (ramp) 0.25 0.2 0.15 0.05 1.5 0.5 ength im Profile three (half-sine): 0.25 0.2 0.15 0.1 0.05 0.5 1.5 length m)
Profile one (step) 0.25 02 0.15 0.1 0.05 005 0.5 0.5 1.5 ength im) Profile two (ramp) 0.25 0.2 0.15 0.05 1.5 0.5...
Q5 The equation of the motion of the mechanical system shown in the following figure is...
Q5 The equation of the motion of the mechanical system shown in the following figure is governed by the following differential equation d2 x dx m7+9+= -f(t) - 3kx dt2 dt where m, C and k are mass, damping coefficient and spring constant, respectively. Consider the system with m = 10 kg, c = 80 Ns/m, k = 50 N/m, and the system is at rest at time t = 0 s. f(t) is the external force acting on the...
Question 27 a k = 50 N/m hellllile osno 0.5 kg Submit x= -0.5 m X...
Question 27 a k = 50 N/m hellllile osno 0.5 kg Submit x= -0.5 m X = 0.0 m X = 0.5 m A block of mass 0.5 kg on a horizontal surface is attached to a horizontal spring of negligible mass and spring constant 50 N/m. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. When the spring is unstretched, the block is located at...
What is the Laplace Transform of below function ? 0.5 o 0.5 1 1.5 2 2.5...
What is the Laplace Transform of below function ? 0.5 o 0.5 1 1.5 2 2.5 3 Time (s) 3.5 4 4.5 5 5.5 Cae-1.551 0.51 s? +(0.571)2 40 OB.( OB. (5-1.5)2 + (410) 0.571 OC (3–1,+0.50 00.2-15742 m OE. None of above
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?...
5. (Inhomogeneous equations: Laplace transforms: Resonance) A spring with spring constant k> 0 is...
5. (Inhomogeneous equations: Laplace transforms: Resonance) A spring with spring constant k> 0 is attached to a m > 0 gram block. The spring starts from rest (x(0) - x'(0) 0 and is periodically forced with force f(t) - A sin(wft), with amplitude A > 0. (a) Write down the differential equation describing the displacement of the spring and the initial condition. (b) Solve the initial value problem from (a) using the Laplace transform. (c) What happens to the solution...
find the general solution (y) using laplace transform
(1 point) Consider a spring attached to a 1 kg mass, damping constant 8 = 5, and spring constant k = 6 The initial position of the spring is 4 metres beyond its resting length, and the initial velocity is -9 m/s. After 1 second, a constant force of 12 Newtons is applied to the system for exactly 2 seconds Set up a differential equation for the position of the spring y...
Question. Systems of ODEs of higher order can be solved by the Laplace transform method. As an important application, typical of many similar mechanical systems, consider coupled vibrating masses on springs. Wrovov The mechanical system in the Figure consists of two bodies of mass 1 on three springs of the same spring constant k and of negligibly small masses of the springs. Also damping is assumed to be practically zero. Then the model of the physical system is the system...
6) The 18 kg mass of a spring-mass system is initially at rest. At time = 0, a 400 N force is applied (toward the right). Spring constant is 100 kN / m, and the viscous damping coefficient is 520 Ns/m Determine the transient response F = (400 N) 1(t) Delay time [HINT: may need to a) graphing calculator, fixed point iteration; or calculator equation solver] b) c) use a m Peak time Maximum overshoot (in mm)
6) The 18...
A single dof vibration system, modeled by a mass of 50 kg, damping coefficient of 300 Ns/m, and spring constant of 5000 N/m, is subjected to periodic displacement excitation u(t) as shown in the figure below. 1. Derive the equation of motion 2. Using Laplace transform, find characteristic equation. 3. Find the undamped and damped natural frequencies. 4. Find the damping ratio. 5. Find the transfer function of output x(t) to the periodic input u(t) using Laplace transform.
Find the function of each graph u(x) and then u(t) and take the
laplace transformation of u(t). Knowing that x=vt
Profile one (step) 0.25 02 0.15 0.1 0.05 005 0.5 0.5 1.5 ength im) Profile two (ramp) 0.25 0.2 0.15 0.05 1.5 0.5 ength im Profile three (half-sine): 0.25 0.2 0.15 0.1 0.05 0.5 1.5 length m)
Profile one (step) 0.25 02 0.15 0.1 0.05 005 0.5 0.5 1.5 ength im) Profile two (ramp) 0.25 0.2 0.15 0.05 1.5 0.5...
Q5 The equation of the motion of the mechanical system shown in the following figure is governed by the following differential equation d2 x dx m7+9+= -f(t) - 3kx dt2 dt where m, C and k are mass, damping coefficient and spring constant, respectively. Consider the system with m = 10 kg, c = 80 Ns/m, k = 50 N/m, and the system is at rest at time t = 0 s. f(t) is the external force acting on the...
Question 27 a k = 50 N/m hellllile osno 0.5 kg Submit x= -0.5 m X = 0.0 m X = 0.5 m A block of mass 0.5 kg on a horizontal surface is attached to a horizontal spring of negligible mass and spring constant 50 N/m. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. When the spring is unstretched, the block is located at...
What is the Laplace Transform of below function ? 0.5 o 0.5 1 1.5 2 2.5 3 Time (s) 3.5 4 4.5 5 5.5 Cae-1.551 0.51 s? +(0.571)2 40 OB.( OB. (5-1.5)2 + (410) 0.571 OC (3–1,+0.50 00.2-15742 m OE. None of above
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?...
5. (Inhomogeneous equations: Laplace transforms: Resonance) A spring with spring constant k> 0 is attached to a m > 0 gram block. The spring starts from rest (x(0) - x'(0) 0 and is periodically forced with force f(t) - A sin(wft), with amplitude A > 0. (a) Write down the differential equation describing the displacement of the spring and the initial condition. (b) Solve the initial value problem from (a) using the Laplace transform. (c) What happens to the solution...
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