Differential equation solve classical method

x'' + 2x' + x = 5exp(-t) + t for t greater/equal to zero; x(0)=2; x'(0)=1 and identify critically damp, overdamp or under damped thank you

Uniqueness of I

Prove the uniquemess of I, the nxn identity matrix.

true or false

1. Every linear system of four equations in five unknowns has infinitely many solutions. 2. If two systems of linear equations have augmented matrices that row reduce to the same reduced row echelon form, then they have the same solution set. 3. If a system of m linear equations in four unknowns has a unique solution, then m must be greater than or equal to four. 4. If a system of m linear equations in four unknowns has no solutions, then m must be greater than or equal to four. 5. A system of three linear equations in three unknowns has a unique solution if and only if its coefficient matrix is row equivalent to the 3x3 identity matrix.

Linear systems

A home handyman decides to fix his own tv set, despite the warning on the back cover. He switches it off, pulls the plug, removes the back cover, reaches inside, and recieves a large electrical shock. Assume he touches the inside within 2 seconds after switching of the set. The dc source (figure 4) that drives the sets picture tube is 20KV ; C is 1uF and R is 1m ohm. Why did he get a shock? If his body resistance was 2M ohms, how much energy did his body absorb if he held on for 10 s?

Differential equations

Refer to figure 2 in attachment a) write the equations of motion for the mechanical system ( i think i got that right, but im not sure with my answer) ****PLEASE SHOW YOUR FREE-BODY FOR EACH MASS****THANKS B) take the Laplace transform of these equations, arrange them in matrix form, solve for the displacement x2(t), and find the transfer function T(s)= X1(s)/F(s) C) Using the concept of the transfer function, find X1(t) if f(t) = 4u(t) N. thank you for your help! THE SECOND ATTACHMENT SHOULD HELP IN EXPLAIN THE TRANSFER FUNCTION