12
into a system of first-order equations in which does not appear explicitly. 5. Write s with initial conditions into a system of first-order equations in which does not appear explicitly. 5...
(1 point) Write the given second order equation as its equivalent system of first order equations. u" – 1.5u - 1.5u = -7 sin(3), 4(1) = 5, (1) = 6.5 Use v to represent the "velocity function", i.e. v = u(t). Use v and u for the two functions, rather than u(t) and v). (The latter confuses webwork. Functions like sin(t) are ok.) u = Now write the system using matrices: and the initial value for the vector valued function...
3. Consider the first-order system of differential equations: (a) Find the general real-valued solutions (b) Find the unique real-valued solution with initial conditions yi (0) = 5 and y2(0) = 4.
7. Systems of first order equations higher order. Consider the system can sometimes be transformed into a single equation of xf xx12x2 = -2x1 + X2, (a) Solve the first equation for x2 and substitute into the second equation, thereby obtain- ing a second order equation for x1. Solve this equation for x1 and then determine x2 also (b) Find the solution of the given system that also satisfies the initial conditions x\ (0) = 2, x2 (0)= 3
(1 point) Write the given second order equation as its equivalent system of first order equations. u" +5.5u' – 2.5u = -7.5 sin(3t), u(1) = -1, u'(1) = 0.5 Use v to represent the "velocity function", i.e. v=u't). Use v and u for the two functions, rather than u(t) and v(t)(The latter confuses webwork. Functions like sin(t) are ok.) u = V = Now write the system using matrices: and the initial value for the vector valued function is: u(1)
Problem 5: For the system shown below, write the differential equations for small motions of the system, in terms of the degrees of freedom (x(t),() Mass of the bar is m, and mass of the block is also m. System is set into motion through suitable initial conditions. Once you find the equations of motion in terms of the respective degrees of freedom, write out the natural frequency and the damping ratio for each sub-system, respectively. Problem 5: For the...
as its equivalent system of first order equations 12. Write the given second order equation u" — 21! — 5и —7sin(31), Use v to represent the "velocity function", i.e. v = u'(t) u'(1)1 u(1) -4, as its equivalent system of first order equations 12. Write the given second order equation u" — 21! — 5и —7sin(31), Use v to represent the "velocity function", i.e. v = u'(t) u'(1)1 u(1) -4,
w set 1, page4 o 4 ade ApPL 5. Find a system of differential equations and initial conditions for the currents in the network given below. Assume that all initial currents are zero. Solve for the currents in the network. 10Ω 5Ω w set 1, page4 o 4 ade ApPL 5. Find a system of differential equations and initial conditions for the currents in the network given below. Assume that all initial currents are zero. Solve for the currents in...
Solve the following system of first order differential equations: Given the system of first-order differential equations ()=(3) () determine without solving the differential equations, if the origin is a stable or an unstable equilibrium. Explain your answer.
L-8 29 -15 22] 111 4 3 2 1 10. The differential equations of high order: 2 And boundary conditions fo)-0, f' (0)-0, f'(5)-1, g(o)-1.5, g(5)-1 Can be solved using The Shooting-Newton-Raphson and multivariable Runge-Kutta for a value of (y-1.7), re write the system of equations in the canonical form (i.e. as a set of ODES of first order and its boundary conditions). It is not required to solve the equations, just list the system of first order differential equations...
4. Find the value of x(0.3) for the coupled first order differential equations together with initial conditions dx x(0) 0 and y(0)=1 sint, dt 4. Find the value of x(0.3) for the coupled first order differential equations together with initial conditions dx x(0) 0 and y(0)=1 sint, dt