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Hoochie [10]
3 years ago
11

A mass weighing 3 lb stretches a spring 3 in. If the mass is pushed upward, contracting the spring a distance of 1 in and then s

et in motion with a downward velocity of 2 ft/s, and if there is no damping, find the positionu of the mass at any timet. Determine the frequency, period, amplitude, and phase of the motion.
Mathematics
1 answer:
Bas_tet [7]3 years ago
3 0

Answer:

Step-by-step explanation:

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}}

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Answer:

The given function symmetric about the y-axis.

Step-by-step explanation:

The given function is

r=9\sin 7\theta                .... (1)

1. Symmetry about the x-axis: If the point (r, θ ) lies on the graph, then the point  (r,-θ ) or (-r, π - θ ) also lies on the graph.

2. Symmetry about the y-axis: If the point (r, θ ) lies on the graph, then the point (r,π - θ ) or (-r, -θ ) also lies on the graph.

3. Symmetry about the origin: If the point (r, θ ) lies on the graph, then the point (-r, θ ) or (r, π + θ ) also lies on the graph.

Put (r, -θ ) in the given function.

r=9\sin 7(-\theta)=-9\sin 7\theta=-r\neq r

Therefore it is not symmetric about x-axis.

Put (-r, -θ ) in the given function.

-r=9\sin 7(-\theta)=-9\sin 7\theta=-r

Therefore it is symmetric about y-axis.

Put (-r,θ ) in the given function.

-r=9\sin 7(\theta)=r\neq -r

Therefore it is not symmetric about the origin.

3 0
3 years ago
Gavin and his three friends want to share 1/3of cake equally. Gavin says that each friend will get 1/9 of the cake. Use the drop
Alexxandr [17]

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Step-by-step explanation:

Given

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So, there are 4 members to distribute the cake

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So, each member get one-twelvefth of the given cake.

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Answer:

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777dan777 [17]

Answer:

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Number of red socks = 2

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The formula used to calculate probability is: Probability=\frac{Number \ of \ favourable \ outcomes}{Total \ number \ of  \ outcomes}

We are given you draw out a  sock, return it, and draw out a second sock.

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Using formula:

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