Select the correct answer.

A mass weighing 11 lb stretches a spring 4in. The mass is pulled down an additional 3 in and is then set in motion with an initi

Shtirlitz [24]

Answer:

a) $x(t) = 2.845\cdot \cos \left(1.732\cdot t -0.473\pi \right)$ , b) $T = 3.628\,s$ , $A = 2.845\,ft$ , $\phi = -0.473\pi$

Explanation:

a) The system mass-spring is well described by the following equation of equilibrium:

$\Sigma F = k\cdot x - m\cdot g = m\cdot a$

After some handling in physical and mathematical definition, the following non-homogeneous second-order linear differential equation:

$\frac{d^{2}x}{dt^{2}}+\frac{k}{m}\cdot x = g$

The solution of this equation is:

$x (t) = A\cdot \cos \left(\sqrt{\frac{k}{m} } \cdot t + \phi\right)$

The velocity function is:

$v(t) = \sqrt{\frac{k}{m} }\cdot A\cdot \sin \left(\sqrt{\frac{k}{m} }\cdot t +\phi \right)$

Initial conditions are:

$x(0\,s) = 0.25\,ft, v(0\,s) = -5\,\frac{ft}{s}$

Equations at $t = 0\,s$ are:

$0.25\,ft = A\cdot \cos \phi\\-5\,\frac{ft}{s} =\sqrt{\frac{k}{m} }\cdot A\cdot \sin \phi$

The spring constant is:

$k = \frac{11\,lbf}{0.333\,ft}$

$k = 33\,\frac{lbf}{ft}$

After some algebraic handling, amplitude and phase angle are found:

$\phi = -0.473\pi$

$A = 2.845\,ft$

The position can be described by this function:

$x(t) = 2.845\cdot \cos \left(1.732\cdot t -0.473\pi \right)$

b) The period of the motion is:

$T = \frac{2\pi}{\sqrt{\frac{k}{m} } }$

$T = 3.628\,s$

The amplitude is:

$A = 2.845\,ft$

The phase of the motion is:

$\phi = -0.473\pi$

8 0

4 years ago

List four landforms created by wave erosion?

choli [55]

A Headland,a Sea Cave,a Sea Arch, and a sea cut cliff.

8 0

3 years ago

15 points just because i’m feeling like super nice right now! brainly if you tell me how your day was? <3

kifflom [539]

Answer:

it is good so far

i just passed my math test

Explanation:

5 0

3 years ago

When you jump upward, your hang time is the time your feet are off the ground. Does hang time depend on the vertical component o

hjlf

Answer:

It only depends on the vertical component

Explanation:

Hello!

The horizontal component will tell you how much you travel in that direction.

You could have a large horizontal velocity, but if the vertical velocity is zero, you will never be out of the ground. Similarly, you could have a zero horizontal velocity, but if you have a non-zero vertical velocity you will be some time off the ground. This time can be calculated by two means, one is using the equation of motion (position as a function of time) and the other using the velocity as a fucntion of time.

For the former you must find the time when the position is zero.

Lets consider the origin of teh coordinate system at your feet

y(t) = vt - (1/2)gt^2

We are looking for a time t' for which y(t')=0

0 = vt' - (1/2)gt'^2

vt' = (1/2)gt'^2

The trivial solution is when t'=0 which is the initial position, however we are looking for t'≠0, therefore we can divide teh last equation by t'

v = (1/2)gt'

Solving for t'

t' = (2v/g)

7 0

3 years ago

Determine the number of bonding electrons and the number of nonbonding electrons in the structure of of2.

Gnoma [55]

OF2 -
O has 6 electrons in outer shell and F has 7 in its outer shell 
Therefore, you have to account for 20 electrons total in the 
structure (7+7+6 = 20) 
therefore draw it linear first. F ---- O-----F 
The two bonds take care of 4 electrons now you have to add another 16. 
Therefore 3 lone pairs on each F and 2 lone pair on O. 
If you check for formal charges, all the atoms are neutral 
F will have 3 lone pairs + 1 bond = 7 electrons (bond = 1/2 electron for formal charge distribution) therefore both the F's are neutral 
Now look at the O: it should have 6.. it has two lone pair and 2 bonds = 4 electrons and 2 bonds = 1 electron each = 2 electrons from bonds = 6 total electrons for formal charge which is exactly the # it should have. There is no need for any double bond in this as there are no charges to be separated. 
Now if u look at the # of domains around O you will see if you include the lone pairs it has a sp3 hybridization (4 domains) therefore a tetrahedron which has 2 lone pairs and 2 bonds.. since there are two lone pairs, the lone pair/bond pair repulsion is so high it is going to repel the two Fluorines and form a bent structure, looks a lot like H2O.

4 0

3 years ago

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