Question

Suppose a spring with spring constant 7 N/m is horizontal and has one end attached to a wall and the other end attached to a 3kg mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is 3 N.s/m, and the forcing function is F(t) = 9sin (3t).

Answer 1

can anyone help me with this please

Answer 2

i know that it is 3x''+3x'+7x = 9sin 3t

Answer 3

What is the question?

Answer 4

Find a particular solution to the nonhomogeneous differential equation .
xp =

Answer 5

Use the method of undetermined coefficients. As a start, try
\[x_p=A\sin(3t)+B\cos(3t).\]
Find \(x_p'\text{ and }x_p'',\) substitute them into the equation, and solve for A and B.

Answer 6

Yes I tried that but doesn't work out for me ..!!

Answer 7

test

Answer 8

\[\begin{align*}x_p&=A\sin(3t)+B\cos(3t)\\
x_p'&=3A\cos(3t)-3B\sin(3t)\\
x_p''&=-9A\sin(3t)-9B\cos(3t)
\end{align*}\]
\[3x''+3x'+7x=9\sin(3t)\\
[-27A\sin(3t)-27B\cos(3t)]+[9A\cos(3t)-9B\sin(3t)]+[7A\sin(3t)+7B\cos(3t)]\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=9\sin(3t)\\
(-20A+9B)\sin(3t)+(-20B+9A)\cos(3t)=9\sin(3t)\]
Can you solve for A and B now?

Answer 9

thank you i got it finally cheers for your help !!