$m=\frac{3}{32}\\ \gamma =0\text{ damping constant.}\\ k=\frac{3}{\frac{1}{4}}=12\\ F(t)=0\\ \text{so equation of motion is }\\ mu''+\gamma u'+ku=F(t)\\ \frac{3u''}{32}+12u=0\\ u''+128u=0\\ \text{and initial conditions are}\\ u(0)=-\frac{1}{12}\\ u'(0)=2\\ u''+128u=0\\ \text{characterstic equation is}\\ r^2+128=0\\ \text{roots are }\\ r=\pm 8\sqrt{2}i\\ \text{therefore general solution is}\\ u(t)=A\cos8\sqrt{2}t+Bsin8\sqrt{2}t\\ \text{using initial conditions we get}\\ A=-\frac{1}{12}\\ B=\frac{\sqrt{2}}{8}\\ \text{therefore solution is }\\ u(t)=-\frac{1}{12}\cos8\sqrt{2}t+\frac{\sqrt{2}}{8}\sin8\sqrt{2}t\\
{hence}\\R=\sqrt{\frac{11}{288}}\\\\\sigma=\pi - \tan^{-1}\frac{1}{\sqrt{2}}\\\\\omega_0=8\sqrt{2}\\T=\frac{4}{4\sqrt{2}}$

3 0

2 years ago

Hi i am having trouble with this question can some one help me on it i heard this app really helps you understand question i mig

Evgen [1.6K]

Answer:

n = -1

Step-by-step explanation:

Guess your question is to find n

Given:

-6 + 3n = -9

Add 6 to both sides

-6 + 6 + 3n = -9 + 6

3n = -3

Divide both sides by 3

n = -3 / 3

= -1

n = -1

Check:

-6 + 3n = -9

-6 + 3(-1) = -9

-6 - 3 = -9

- 9 = - 9

6 0

2 years ago