above is the answer, because this is unit step function, and we know initial value is zero, so I can separate the function into two part just like following q5, and then use d/dt to equate both side. but I cannot get the correct value, please help me
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above is the answer, because this is unit step function, and we
know initial value is...
over Ky(t) ==0) Assume in the following questions that M = 1, D = 2 and...
over Ky(t) ==0) Assume in the following questions that M = 1, D = 2 and K = 2. 5. Let to > 0, and let P be the pulse input of duration to given by P(t) = Po(u(t) – uſt – to)) where Po > 0. (a) Find the system pulse response Ypul(t) from the input x(t) = P(t), for all t > 0, assuming zero initial conditions. You may assume that the pulse response has the form Ypu(t)...
Problem 2 Determine the transfer function 01(s)/M(s) for the shaft-gear mechanical system in the figure, where...
Problem 2 Determine the transfer function 01(s)/M(s) for the shaft-gear mechanical system in the figure, where 1(s) and Ms) are the Laplace transforms of the angle 01(t) and of the moment m(t). Use the time-domain mathematical model of this system. Known are J1, ki, J2, c, k2, Ni and N2. N. 1000 0,m 0 000 N Problem 3 By using the transfer function 1(s)/Ms), determined in Problem 2, calculate and plot 01(t) using the step input command of MATLAB. Known...
1. Solve the initial value problem for a damped mass-spring system acted upon by a sinusoidal...
1. Solve the initial value problem for a damped mass-spring system acted upon by a sinusoidal force for some time interval f(t) = {10 sin 2t 0 0<t< y(0) 1, y'(0) -5 y"2y' 2y f(t), Tt zusor= 2. Consider two masses and three springs without no external force. The resulting force balance can be expressed as two second order ODES shown as below. mx=-(k k2)x1+ kzx2 m2x2 (k2k3)x2 + k2x1 15 If m 2,m2 ki = 1,k2 = 3, k3...
Consider the following initial value problem: 1. Use Euler's explicit scheme to solve the above initial value probl...
Consider the following initial value problem: 1. Use Euler's explicit scheme to solve the above initial value problem with time step h= 0.5. Express all the computed results with a precision of three decimal places. 2. The analytical or exact solution is compute the absolute error at each tivalue. Express all the computed results with a precision of three decimal places. 3. Write a matlab function that solves the above (IVP) using (RK2.M) for arbitrary time-step h. y(t) ly(0) 3...
Question three The figure below shows a unit step response of a second order system. From...
Question three The figure below shows a unit step response of a second order system. From the graph of response find: 1- The rise timet, 2- The peak timet, 3- The maximum overshoot Mp 4- The damped natural frequency w 5. The transfer function. Hence find the damping ratio ζ and the natural frequency ah-Find also the transfer function of the system. r 4 02 15 25 35 45 Question Four For the control system shown in the figure below,...
+ (3) ar2 2. Recall from lectures that the governing PDE for vibrations of a circular...
+ (3) ar2 2. Recall from lectures that the governing PDE for vibrations of a circular drum lid is 1 au 1 ay c? + 012 72 302 for r € (0,R), 0€ (-2,7), and t > 0, and the boundary condition is (R, 6,t) = 0 for t>0 and -150<7. rar (4) You will search for a solution of the form v(r,0,t) = G(r) sin(30) cos(w t), (5) for a function G that satisfies the ODE m2 G" +rG'...
Here we consider the two masses m1 and m2 connected this time by springs of stiffnesses...
Here we consider the two masses m1 and m2 connected this time by
springs of stiffnesses k1, k2 and k3 as shown in the figure below.
The movement of each of the 2 masses relative to its position of
static equilibrium is designated by x1(t) and x2(t).
1. Demonstrate that the differential equation whose unknown is
the displacement x1(t) is written as follows:
2. Determine the second differential equation whose unknown is
the displacement x2(t).
3. Determine the free oscillatory...
O/3 points | Previous Answers WWCMDiffEQLinAlg1 7.5.006. My Not Suppose that masses mi and m2 are...
O/3 points | Previous Answers WWCMDiffEQLinAlg1 7.5.006. My Not Suppose that masses mi and m2 are only connected by two springs as in the figure below, but add an external force of cos(wt) that acts on m2. Let mi = 2, m2 = 1, ki =4 and k12 2 k2 my m. does resonance occur? (Enter your answers as a comma-separated list.) For what forcing frequencies -k - k17 k12 m1 0 K1 M. K Y -k12 f2(t) k12 m2...
a) i. Express in terms of the unit step function, the piecewise continuous causal functions (2t2,...
a) i. Express in terms of the unit step function, the piecewise continuous causal functions (2t2, Ost<3 F(t) = {t + 4, 3 st<5 9, t25 [3 marks] ii. Use Laplace transforms to solve the initial value problem a) 7" + 16y = 4cos3t + s(t – 1/3) where y(0) = 0 and y'(0) = 0. [7 Marks) E.K. Donkoh (Ph.D) or [7 marks) B) y' – 3y = F(t), where y(0) = 0 and (sint, Osts F(t) = 1,...
Differentiel equations We consider here, the two masses m1 and m2 connected this time by springs...
Differentiel equations
We consider here, the two masses m1 and m2 connected this time
by springs of stiffnesses k1, k2 and k3 as indicated in the figure
below. We denote by x1 (t) and x2 (t) the movement of each of the 2
masses relative to its static equilibrium position.
1. Prove that the differential equation whose unknown is the
displacement x1 (t) is written in the following form:
2. Deduce the second differential equation whose unknown is the
displacement...
over Ky(t) ==0) Assume in the following questions that M = 1, D = 2 and K = 2. 5. Let to > 0, and let P be the pulse input of duration to given by P(t) = Po(u(t) – uſt – to)) where Po > 0. (a) Find the system pulse response Ypul(t) from the input x(t) = P(t), for all t > 0, assuming zero initial conditions. You may assume that the pulse response has the form Ypu(t)...
Problem 2 Determine the transfer function 01(s)/M(s) for the shaft-gear mechanical system in the figure, where 1(s) and Ms) are the Laplace transforms of the angle 01(t) and of the moment m(t). Use the time-domain mathematical model of this system. Known are J1, ki, J2, c, k2, Ni and N2. N. 1000 0,m 0 000 N Problem 3 By using the transfer function 1(s)/Ms), determined in Problem 2, calculate and plot 01(t) using the step input command of MATLAB. Known...
1. Solve the initial value problem for a damped mass-spring system acted upon by a sinusoidal force for some time interval f(t) = {10 sin 2t 0 0<t< y(0) 1, y'(0) -5 y"2y' 2y f(t), Tt zusor= 2. Consider two masses and three springs without no external force. The resulting force balance can be expressed as two second order ODES shown as below. mx=-(k k2)x1+ kzx2 m2x2 (k2k3)x2 + k2x1 15 If m 2,m2 ki = 1,k2 = 3, k3...
Question three The figure below shows a unit step response of a second order system. From the graph of response find: 1- The rise timet, 2- The peak timet, 3- The maximum overshoot Mp 4- The damped natural frequency w 5. The transfer function. Hence find the damping ratio ζ and the natural frequency ah-Find also the transfer function of the system. r 4 02 15 25 35 45 Question Four For the control system shown in the figure below,...
+ (3) ar2 2. Recall from lectures that the governing PDE for vibrations of a circular drum lid is 1 au 1 ay c? + 012 72 302 for r € (0,R), 0€ (-2,7), and t > 0, and the boundary condition is (R, 6,t) = 0 for t>0 and -150<7. rar (4) You will search for a solution of the form v(r,0,t) = G(r) sin(30) cos(w t), (5) for a function G that satisfies the ODE m2 G" +rG'...
Here we consider the two masses m1 and m2 connected this time by
springs of stiffnesses k1, k2 and k3 as shown in the figure below.
The movement of each of the 2 masses relative to its position of
static equilibrium is designated by x1(t) and x2(t).
1. Demonstrate that the differential equation whose unknown is
the displacement x1(t) is written as follows:
2. Determine the second differential equation whose unknown is
the displacement x2(t).
3. Determine the free oscillatory...
O/3 points | Previous Answers WWCMDiffEQLinAlg1 7.5.006. My Not Suppose that masses mi and m2 are only connected by two springs as in the figure below, but add an external force of cos(wt) that acts on m2. Let mi = 2, m2 = 1, ki =4 and k12 2 k2 my m. does resonance occur? (Enter your answers as a comma-separated list.) For what forcing frequencies -k - k17 k12 m1 0 K1 M. K Y -k12 f2(t) k12 m2...
a) i. Express in terms of the unit step function, the piecewise continuous causal functions (2t2, Ost<3 F(t) = {t + 4, 3 st<5 9, t25 [3 marks] ii. Use Laplace transforms to solve the initial value problem a) 7" + 16y = 4cos3t + s(t – 1/3) where y(0) = 0 and y'(0) = 0. [7 Marks) E.K. Donkoh (Ph.D) or [7 marks) B) y' – 3y = F(t), where y(0) = 0 and (sint, Osts F(t) = 1,...
Differentiel equations
We consider here, the two masses m1 and m2 connected this time
by springs of stiffnesses k1, k2 and k3 as indicated in the figure
below. We denote by x1 (t) and x2 (t) the movement of each of the 2
masses relative to its static equilibrium position.
1. Prove that the differential equation whose unknown is the
displacement x1 (t) is written in the following form:
2. Deduce the second differential equation whose unknown is the
displacement...
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