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![free body diagram of mass my Equating forces, we get 1 m, ², + blå, ²2) + 4, 2, = falt) ] frost me d](http://img.homeworklib.com/questions/d96bd7a0-952a-11ea-9f5b-13290722bcac.png?x-oss-process=image/resize,w_560)
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Figure 4 shows a two-mass translational mechanical system. The applied force falt) acts on mass mi....
3. Consider the spring - mass system shown below, consisting of two masses mi and ma sus- pended ...
3. Consider the spring - mass system shown below, consisting of two masses mi and ma sus- pended from springs with spring constants ki and k, respectively. Assume that there is no damping in the system. a) Show that the displacements z1 and 2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above resuit to show that the spring-mass system satisfies the following fourth order differential equation. and ) Find the general solution...
8.9 The MEMS of Figure 8.29 is formed of two shuttle masses mi and m2 coupled by a serpentine spr...
8.9 The MEMS of Figure 8.29 is formed of two shuttle masses mi and m2 coupled by a serpentine spring of stiffness k and supported separately by two pairs of identical beam springs- each beam has a stiffness ki. The shuttle masses are subjected to viscous damping individually through substrate interaction-the damping coefficient is c, and an electrostatic force f acts on mi. Use a lumped-parameter model of this MEMS device and obtain a state-space model for it by considering...
3. Consider the spring - mass system shown below, consisting of two masses mi and m2 sus- pended ...
3. Consider the spring - mass system shown below, consisting of two masses mi and m2 sus- pended from springs with spring constants ki and k2, respectively. Assume that there is no damping in the system. a) Show that the displacements ai and r2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above result to show that the spring-mass system satisfies the following fourth order differential equation and c) Find the general solution...
2. A two-mass translational mechanical system has the following mathematical model: mž +bi,+k, (*; - x)=f,0)...
2. A two-mass translational mechanical system has the following mathematical model: mž +bi,+k, (*; - x)=f,0) m,ž, +b,X, +k, (x2 – x)+k,x, = 0 The displacements Xi and X2 are measured from their respective equilibrium positions. An external force falt) is applied to the system. Sketch a possible configuration of the two-mass mechanical system. Label all elements and show the positive convention for displacement in your sketch. (Hint verify the system model by applying Newton's laws.)
4. Two masses mi and m2 are connected to three springs of negligible mass having spring constants...
4. Two masses mi and m2 are connected to three springs of negligible mass having spring constants k1, k2 and k3, respectively. x2=0 Il k, Let xi and x2 represent The motion of the equations: displacements of masses mi and m2 from their equilibrium positions . coupled system is represented by the system of second-order differential d2x dt2 d2x2 Using Laplace transform to solve the system when k1 1 and x1(0) = 0, xi (0)--1 , x2(0) = 0, x(0)-1....
3. The following figure shows the block diagram of a mechanical translational system k1 U3 m1...
3. The following figure shows the block diagram of a mechanical translational system k1 U3 m1 (a) Draw free body diagrams for each of the masses. Bearing in mind that the force due to spring is proportional to its length and the force due to friction is proportional to velocity, label each of the forces acting upon each body. (b) Develop the dynamical equations for the system.
Figure 3 shows a lumped-parameter representation of a concept for a MEMS "tuning fork gyro- scope"...
Figure 3 shows a lumped-parameter representation of a concept for a MEMS "tuning fork gyro- scope" for measuring angular velocity. Displacement 21(t), 22(t), and y(t) are absolute positions of the inertia elements m, m2, and m3, respectively, and are measured from their static equi- librium positions where there is no deflection in the springs. The system friction is represented by three ideal lumped dashpot elements bi, by, and by. Two external forces fi(t) and fa(t) are applied to masses m,...
Figure 1 shows a system comprising a bar with mass m=12 kg and the length of...
Figure 1 shows a system comprising a bar with mass m=12 kg and
the length of the bar L=2 m, two springs with stiffness k_t=1000
N-m/rad and k=2000 N/m, one damper with damping coefficient c=50
N-s/m and two additive masses at the end of the bar, where each
mass (M) is equal to 50 kg. The rotation about the hinge A,
measured with respect to the static equilibrium position of the
system is θ(t). The system is excited by force...
QUESTION 4 (140 marks) Determine the damped frequency of the spring-mass system schematically illustrated below if...
QUESTION 4 (140 marks) Determine the damped frequency of the spring-mass system schematically illustrated below if the spring stiffness is 3000 N/m and the damping coefficient c is set at 320 Ns/m. If a periodic 260 N force is applied to the mass at a frequency of 2 Hz, determine the amplitude of the forced vibration. Spring Viscous damper 35 kg Figure 4
6.(16) Consider the spring-mass system shown, consisting of two unit masses m, and my suspended from...
6.(16) Consider the spring-mass system shown, consisting of two unit masses m, and my suspended from springs with constants k, and ky, respectively. Assuming that there is no damping in the system, the displacement y(t) of the bottom mass m, from its equilibrium positions satisfies the 4-order equation (4) y2 + k + k)y + k_k2yz = e-2, where f(t) = e-2 is an outside force driving the motion of m. If a 24 N weight would stretch the top...
3. Consider the spring - mass system shown below, consisting of two masses mi and ma sus- pended from springs with spring constants ki and k, respectively. Assume that there is no damping in the system. a) Show that the displacements z1 and 2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above resuit to show that the spring-mass system satisfies the following fourth order differential equation. and ) Find the general solution...
8.9 The MEMS of Figure 8.29 is formed of two shuttle masses mi and m2 coupled by a serpentine spring of stiffness k and supported separately by two pairs of identical beam springs- each beam has a stiffness ki. The shuttle masses are subjected to viscous damping individually through substrate interaction-the damping coefficient is c, and an electrostatic force f acts on mi. Use a lumped-parameter model of this MEMS device and obtain a state-space model for it by considering...
3. Consider the spring - mass system shown below, consisting of two masses mi and m2 sus- pended from springs with spring constants ki and k2, respectively. Assume that there is no damping in the system. a) Show that the displacements ai and r2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above result to show that the spring-mass system satisfies the following fourth order differential equation and c) Find the general solution...
2. A two-mass translational mechanical system has the following mathematical model: mž +bi,+k, (*; - x)=f,0) m,ž, +b,X, +k, (x2 – x)+k,x, = 0 The displacements Xi and X2 are measured from their respective equilibrium positions. An external force falt) is applied to the system. Sketch a possible configuration of the two-mass mechanical system. Label all elements and show the positive convention for displacement in your sketch. (Hint verify the system model by applying Newton's laws.)
4. Two masses mi and m2 are connected to three springs of negligible mass having spring constants k1, k2 and k3, respectively. x2=0 Il k, Let xi and x2 represent The motion of the equations: displacements of masses mi and m2 from their equilibrium positions . coupled system is represented by the system of second-order differential d2x dt2 d2x2 Using Laplace transform to solve the system when k1 1 and x1(0) = 0, xi (0)--1 , x2(0) = 0, x(0)-1....
3. The following figure shows the block diagram of a mechanical translational system k1 U3 m1 (a) Draw free body diagrams for each of the masses. Bearing in mind that the force due to spring is proportional to its length and the force due to friction is proportional to velocity, label each of the forces acting upon each body. (b) Develop the dynamical equations for the system.
Figure 3 shows a lumped-parameter representation of a concept for a MEMS "tuning fork gyro- scope" for measuring angular velocity. Displacement 21(t), 22(t), and y(t) are absolute positions of the inertia elements m, m2, and m3, respectively, and are measured from their static equi- librium positions where there is no deflection in the springs. The system friction is represented by three ideal lumped dashpot elements bi, by, and by. Two external forces fi(t) and fa(t) are applied to masses m,...
Figure 1 shows a system comprising a bar with mass m=12 kg and
the length of the bar L=2 m, two springs with stiffness k_t=1000
N-m/rad and k=2000 N/m, one damper with damping coefficient c=50
N-s/m and two additive masses at the end of the bar, where each
mass (M) is equal to 50 kg. The rotation about the hinge A,
measured with respect to the static equilibrium position of the
system is θ(t). The system is excited by force...
QUESTION 4 (140 marks) Determine the damped frequency of the spring-mass system schematically illustrated below if the spring stiffness is 3000 N/m and the damping coefficient c is set at 320 Ns/m. If a periodic 260 N force is applied to the mass at a frequency of 2 Hz, determine the amplitude of the forced vibration. Spring Viscous damper 35 kg Figure 4
6.(16) Consider the spring-mass system shown, consisting of two unit masses m, and my suspended from springs with constants k, and ky, respectively. Assuming that there is no damping in the system, the displacement y(t) of the bottom mass m, from its equilibrium positions satisfies the 4-order equation (4) y2 + k + k)y + k_k2yz = e-2, where f(t) = e-2 is an outside force driving the motion of m. If a 24 N weight would stretch the top...
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