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2. Forced vibrations with damping is described by the equation mu” (t) + yu (t) +...
Spring mass damper system with forced response, the forced system given by the equation For damping...
Spring mass damper system with forced response, the forced system given by the equation For damping factor:E-0.1 ; mass; m-| kg: stiffness of spring; k-100 Nm; f-| 00 N; ω Zun; initial condition: x (0)-2 cms; r(0) = 0. fsincot Task Marks 1. Write down the reduced equation into 2first orderns Hand written equations differential equations 2. Rearrange equation (1) with the following generalized equation 250, x+osinor calculations 3. Calculate the value of c calculations Hand calculations 4. Using the...
Problem 5. Consider the following second order linear differential equation f"(t)-f'(t) +f(t) kt ...
Problem 5. Consider the following second order linear differential equation f"(t)-f'(t) +f(t) kt which models a forced oscillation in a damping material. For example, imagine moving your hand back and forth underwater. Write this equation as a set of coupled first order equations by doing the following: ·Define a new function g = f'(t). This gives you one of the two coupled equations. . Use the given ODE, g, and its derivatives to write the second first order equation. Both...
vibrations The given equation represents an undamped forced two degrees of freedom system. (a) Decouple the...
vibrations
The given equation represents an undamped forced two degrees of freedom system. (a) Decouple the equation and find the generalized mass [Ml; stiffiess [K]; force |F) while the generalized coordinates are, (a).(b) Determine the steady state response. ,6 -21 (31 2.
8. Consider the LTI system described by the differential equation in Problem 2.5-1. Solve the (forced)...
8. Consider the LTI system described by the differential equation in Problem 2.5-1. Solve the (forced) response of the system to the following everlasting signals: (a) ft) 1, (b) ftet, (c) f(t) = 100cos(2t- 60°) Using the classical method, solve 2.5-1 (D +7D+12) ye) (D+ 2)f(¢} (0*)= 0, s(0+ ) = 1, and if the input f(t) is if the initial conditions are
8. Consider the LTI system described by the differential equation in Problem 2.5-1. Solve the (forced) response...
Name: I.D. #: HWC2 1) Determine the forced response for the following system described by the...
Name: I.D. #: HWC2 1) Determine the forced response for the following system described by the following differential equation: (5 points) (Show all the steps) d2 de2 y(t)+2 Àre y(t)=xc)+ ax x00 where x(t)=sin2t 1) Determine the forced response for the following system described by the following differential equation: (Show all the steps) (5 points) d2 de2 yt+2 & Y(0)=x(b)+xce) where x(t)=sin2t
2. The angular displacement e(t) of a damped forced pendulum of length 1 swinging in a...
2. The angular displacement e(t) of a damped forced pendulum of length 1 swinging in a vertical plane under the influence of gravity can be modelled with the second order non-homogeneous ODE 0"(t) + 270'(t) +w20(t) = f(t), (2) where wa = g/l. The second term in the equation represents the damping force (e.g. air resistance) for the given constant 7 > 0. The model can be used to approximate the motion of a magnetic pendulum bob being driven by...
3. Consider the forced but undamped system described by the initial value problem u" +u =...
3. Consider the forced but undamped system described by the initial value problem u" +u = 3 cos(wt), 4(0) = 0, 1'0) = 0. a. Find solution for u(t) when w 1. b. Plot the solution u(t) versus t for w = 0.7, 0.8, and 0.9. Describe how the response u(t) changes as w varies. What happens when w gets close to 1? Note that the natural frequency of the system is wo = 1.
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping...
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping c and spring stiffness k: a.- Show that the particular solution for the equation with an applied force fo cos(ot), i.e., Mä+ci+kx=f, cos(or) can be expressed as x )= A cos(ot) + A, sin(or) and find the values of A, and A, that solve the differential equation in terms of M, c, k and fo. 5 points. b. Use the result from part a...
Consider a monochromatic wave on a sting described by an equation Y(x,t) = cos (x -...
Consider a monochromatic wave on a sting described by an equation Y(x,t) = cos (x - t). Assume everything is expressed in SI units. a) Which way the wave is moving, left or right? b) Suppose the same string is now fixed at two ends and has a length 1 m. 2.6 Find three lowest frequencies of standing wave resonances. c) Sketch the profile of the string corresponding to the second standing wave d) What should be the speed of...
Rewrite the second order differential equation, as a system of a first order differential equation. (see...
Rewrite the second order differential equation, as a system of
a first order differential equation. (see picture)
det + sin(a) = 0, 6(0) = el 10) = 0, += [0, 1] 2012 0, t=
Spring mass damper system with forced response, the forced system given by the equation For damping factor:E-0.1 ; mass; m-| kg: stiffness of spring; k-100 Nm; f-| 00 N; ω Zun; initial condition: x (0)-2 cms; r(0) = 0. fsincot Task Marks 1. Write down the reduced equation into 2first orderns Hand written equations differential equations 2. Rearrange equation (1) with the following generalized equation 250, x+osinor calculations 3. Calculate the value of c calculations Hand calculations 4. Using the...
Problem 5. Consider the following second order linear differential equation f"(t)-f'(t) +f(t) kt which models a forced oscillation in a damping material. For example, imagine moving your hand back and forth underwater. Write this equation as a set of coupled first order equations by doing the following: ·Define a new function g = f'(t). This gives you one of the two coupled equations. . Use the given ODE, g, and its derivatives to write the second first order equation. Both...
vibrations
The given equation represents an undamped forced two degrees of freedom system. (a) Decouple the equation and find the generalized mass [Ml; stiffiess [K]; force |F) while the generalized coordinates are, (a).(b) Determine the steady state response. ,6 -21 (31 2.
8. Consider the LTI system described by the differential equation in Problem 2.5-1. Solve the (forced) response of the system to the following everlasting signals: (a) ft) 1, (b) ftet, (c) f(t) = 100cos(2t- 60°) Using the classical method, solve 2.5-1 (D +7D+12) ye) (D+ 2)f(¢} (0*)= 0, s(0+ ) = 1, and if the input f(t) is if the initial conditions are
8. Consider the LTI system described by the differential equation in Problem 2.5-1. Solve the (forced) response...
Name: I.D. #: HWC2 1) Determine the forced response for the following system described by the following differential equation: (5 points) (Show all the steps) d2 de2 y(t)+2 Àre y(t)=xc)+ ax x00 where x(t)=sin2t 1) Determine the forced response for the following system described by the following differential equation: (Show all the steps) (5 points) d2 de2 yt+2 & Y(0)=x(b)+xce) where x(t)=sin2t
2. The angular displacement e(t) of a damped forced pendulum of length 1 swinging in a vertical plane under the influence of gravity can be modelled with the second order non-homogeneous ODE 0"(t) + 270'(t) +w20(t) = f(t), (2) where wa = g/l. The second term in the equation represents the damping force (e.g. air resistance) for the given constant 7 > 0. The model can be used to approximate the motion of a magnetic pendulum bob being driven by...
3. Consider the forced but undamped system described by the initial value problem u" +u = 3 cos(wt), 4(0) = 0, 1'0) = 0. a. Find solution for u(t) when w 1. b. Plot the solution u(t) versus t for w = 0.7, 0.8, and 0.9. Describe how the response u(t) changes as w varies. What happens when w gets close to 1? Note that the natural frequency of the system is wo = 1.
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping c and spring stiffness k: a.- Show that the particular solution for the equation with an applied force fo cos(ot), i.e., Mä+ci+kx=f, cos(or) can be expressed as x )= A cos(ot) + A, sin(or) and find the values of A, and A, that solve the differential equation in terms of M, c, k and fo. 5 points. b. Use the result from part a...
Rewrite the second order differential equation, as a system of
a first order differential equation. (see picture)
det + sin(a) = 0, 6(0) = el 10) = 0, += [0, 1] 2012 0, t=
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