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(b) (3 points) Give an example of a forced spring-mass system which has the same long...
damped forced mass-spring system with m 2, and k 26, under the 2 Consider a influence...
damped forced mass-spring system with m 2, and k 26, under the 2 Consider a influence of an external force F(t)= 82 cos (4t) 1, 7 = a) (8 points) Find the position u(t) of the mass at any time t, if u(0) 6 and u'(0) = 0. b) (4 points) Find the transient solution u(t) and the steady state solution U(t). How would you characterize these two solutions in terms of their behavior in time? We were unable to...
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(4t). a) (8 points) Find the position u(t) of the mass at any time t, if u(0) = 6 and u 0 (0) = 0. b) (4 points) Find the transient solution uc(t) and the steady state solution U(t). How would you characterize these two solutions in terms of their behavior in time?...
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...
Number 2 1. a) The displacement x of a forced spring-mass system is governed by dx...
Number 2
1. a) The displacement x of a forced spring-mass system is governed by dx d2x dt2 + (1 + t)x2 = sint t> 0 x(0) = 0 dx (0) = 0 dt dt Obtain the first four non-zero terms of the solution using the Taylor expansion approach. b) Calculate the position and velocity of the mass at t = 0.5 using the result of part (a). a) The displacement x of a forced spring-mass system is governed by...
For a spring-mass system with forced vibration we have the following equation motion. 100% + 5ỷ...
For a spring-mass system with forced vibration we have the following equation motion. 100% + 5ỷ + 9y 10 cos(St) Initial condition: y(0-0 and у(0)-0 I. Calculate system response analytically.
A free-spring system, damped and not forced hung downwards has the following data: mass = 6 kg, d...
A free-spring system, damped and not forced hung downwards has the following data: mass = 6 kg, damping coefficient of 6 newtons / meter / sec and coefficient of spring (3/2) newton / meter. If it is stretched down 0.6 meters, and fanned upward with a speed of 0.6 m / sec, determine the time it takes to cross to the equilibrium position for the first time. Answer:
3. Consider a system consisting of a Ikg mass connected to a spring with spring co...
3. Consider a system consisting of a Ikg mass connected to a spring with spring co -ION/. and a friction coefficient of 6N/m, subject to an external force of 15 cos 22 newtons). (a) (5 points) Write down the general solution to this system. myll thy't ny=0 "y"+by't loy=0 F(+)= Iscoszt m 2 tlom +10 - (0) (3 points) Label the steady state response and the transient part of the son above (0) (3 points) is the 3 points) Is...
Block A in the figure (Figure 1) has mass 1.00 kg, and block has mass 3.00 kg . The blocks are forced together, compres...
Block A in the figure (Figure 1) has mass 1.00 kg, and block has mass 3.00 kg . The blocks are forced together, compressing a spring S between them; then the system is released from rest on a level, frictionless surface. The spring, which has negligible mass, is not fastened to either block and drops to the surface after it has expanded. Block B acquires a speed of 1.20m/s . A) What is the final speed of block ? -...
mi Question 3. Find the general solution of the forced Mass-Spring system with the following parameters...
mi Question 3. Find the general solution of the forced Mass-Spring system with the following parameters undergoing forcing function F(t). m=2.4 kg, k=38 N/m, F(t)=1.3+3e-t/1.1 The general solution is in the form of X(t)=A1cos(wot)+A2sin(wot)+B1+B2e/11 Enter your answers for w0w0, B1B1 and B2B2 to four decimal places in the appropriate boxes below: w0:00: B1:B1: B2:B2: xlts: A
A horizontal spring mass system is to be constructed. A spring which has a spring constant...
A horizontal spring mass system is to be constructed. A spring which has a spring constant of 3 kg/s2 will be used. The system should be designed so that when it is released and vibrating freely (there is no forcing) the amplitude of its vibrations will decay like ?−0.4t, and it should oscillate with a period of 4 seconds. (Although the motion is oscillatory it is not strictly periodic because the amplitude decays exponentially. In this context "period" refers to...
damped forced mass-spring system with m 2, and k 26, under the 2 Consider a influence of an external force F(t)= 82 cos (4t) 1, 7 = a) (8 points) Find the position u(t) of the mass at any time t, if u(0) 6 and u'(0) = 0. b) (4 points) Find the transient solution u(t) and the steady state solution U(t). How would you characterize these two solutions in terms of their behavior in time? We were unable to...
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...
Number 2
1. a) The displacement x of a forced spring-mass system is governed by dx d2x dt2 + (1 + t)x2 = sint t> 0 x(0) = 0 dx (0) = 0 dt dt Obtain the first four non-zero terms of the solution using the Taylor expansion approach. b) Calculate the position and velocity of the mass at t = 0.5 using the result of part (a). a) The displacement x of a forced spring-mass system is governed by...
For a spring-mass system with forced vibration we have the following equation motion. 100% + 5ỷ + 9y 10 cos(St) Initial condition: y(0-0 and у(0)-0 I. Calculate system response analytically.
3. Consider a system consisting of a Ikg mass connected to a spring with spring co -ION/. and a friction coefficient of 6N/m, subject to an external force of 15 cos 22 newtons). (a) (5 points) Write down the general solution to this system. myll thy't ny=0 "y"+by't loy=0 F(+)= Iscoszt m 2 tlom +10 - (0) (3 points) Label the steady state response and the transient part of the son above (0) (3 points) is the 3 points) Is...
mi Question 3. Find the general solution of the forced Mass-Spring system with the following parameters undergoing forcing function F(t). m=2.4 kg, k=38 N/m, F(t)=1.3+3e-t/1.1 The general solution is in the form of X(t)=A1cos(wot)+A2sin(wot)+B1+B2e/11 Enter your answers for w0w0, B1B1 and B2B2 to four decimal places in the appropriate boxes below: w0:00: B1:B1: B2:B2: xlts: A
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