1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
meriva
3 years ago
6

An undamped spring-mass system contains a mass that weighs and a spring with spring constant . It is suddenly set in motion at b

y an external force of . Determine the position of the mass at any time . Use as the acceleration due to gravity. Pay close attention to the units.

Physics
1 answer:
balandron [24]3 years ago
8 0

Answer:

Explanation:

When all other forces acting on the mass in a damped mass-spring system are grouped together into one term denoted by F(t), the differential equation describing

motion is

Mx''+ βx' + kx = F(t).

Note for an undamped system

β=0,

Then, the differential equation becomes

Mx'' + kx = F(t).

The force is in the form

F=Fo•Sinωo•t

Let solved for the homogeneous or complementary solution, I.e f(t) = 0

Using D operator

MD² + k = 0

MD²=-k

D²=-k/M

Then, D= ±√(-k/m)

D=±√(k/m) •i

So we have a complex root

Therefore, the solution is

x= C1•Cos[√(k/m)t] + C2•Sin[√(k/m)]

This is simple harmonic motion that once again we prefer to write in the form

x(t) = A•Sin[ √(k/M)t + φ]

Where A=√(C1²+C2²)

and angle φ is defined by the equations

sin φ = C1/A and cos φ = C2/A.

Quantity √(k/M), often denoted by ω, is called the angular frequency.

This is called the natural frequency (ωn) of the system

ωn=√(k/M)

ωn²= k/M

Now, for particular solution

Xp=DSinωo•t

Xp' = Dωo•Cosωo•t

Xp"=-Dωo²•Sinωo•t

Now substituting this into

Mx'' + kx = F(t).

M(-Dωo²•Sinωo•t) + k(DSinωo•t)=FoSinωo•t

Now, let solve for D

D(-Mωo²•Sinωo•t +kSinωo•t) = FoSinωo•t

D=Fo•Sinωo•t/(-Mωo²•Sinωo•t +kSinωo•t)

D=Fo•Sinωo•t / Sinωo•t(-Mωo²+k)

D=Fo / (-Mωo²+k)

D=Fo / (k-Mωo²)

Divide through by k

D=Fo/k ÷ (1 -Mωo²/k)

Note from above

ωn²= k/M

Therefore,

D=Fo/k ÷ (1-ωo²/ωn²)

D=Fo/k ÷ [1-(ωo/ωn)²]

Then,

Xp=DSinωo•t

Xp=(Fo/k ÷ [1-(ωo/ωn)²]) Sinωo•t

Then the general solution is the sum of the homogeneous solution and particular solution

Xg(t)=(Fo/k ÷ [1-(ωo/ωn)²]) Sinωo•t + A•Sin[ √(k/M)t + φ]

Check attachment for the graph of homogeneous, particular and general solution.

Also, check for better way of writing the equations.

You might be interested in
Fronts are termed by the temperature of the air mass that overtakes another air mass. A. True B. False
Vikki [24]
A. True
if cold air is replacing warm air it is a cold front and vice versa.
6 0
2 years ago
Read 2 more answers
A 150 kg boy and his bike are traveling 12 m/s when he slams on his breaks and stop at his friend’s house. How much impulse is r
Nataly [62]

Answer:

J = 1800 kg-m/s

Explanation:

Given that,

Mass of a boy, m = 150 kg

Initial velocity of a boy, u = 12 m/s

Finally, it stops, v = 0

We need to find the impulse is required to produce this change in momentum. We know that impulse is equal to the change in momentum. So,

J=m(v-u)\\\\=150\times (0-12)\\\\=-1800\ kg-m/s\\\\|J|=1800\ kg-m/s

So, the impulse is equal to 1800 kg-m/s

4 0
3 years ago
How are elements and<br> compounds identified?
irina1246 [14]

Elements are composed of single atoms and compounds are composed of different elements.

<u>Explanation:</u>

A single atom generally forms an element. It is an individual particle or atom present in the periodic table, mostly it refers with symbol. When two or more elements of different types or same types combine together, it is called as compound.

The compounds can be heterogeneous compounds and homogeneous compounds. Depending upon the combination of elements, this classification is done for compounds. The elements can form a compound by ionic, covalent, metallic or hydrogen bonding. The molecules can also be termed as compounds.

3 0
2 years ago
4. What is the electric field strength 1.4 nm from a charge of 4.7 cC?
pentagon [3]

The electric field strength is 2.16\cdot 10^{26} N/C

Explanation:

The strength of the electric field produced by a single point charge is given by:

E=k\frac{q}{r^2}

where

k=8.99\cdot 10^9 Nm^{-2}C^{-2} is the Coulomb's constant

q is the magnitude of the charge

r is the distance from the charge at which the field strength is calculated

For the charge in the problem, we have:

q=4.7 cC = 0.047 C is the charge

r=1.4 nm = 1.4\cdot 10^{-9} m

Therefore, the electric field strength is

E=(8.99\cdot 10^9)\frac{0.047}{(1.4\cdot 10^{-9})^2}=2.16\cdot 10^{26} N/C

Learn more about electric fields:

brainly.com/question/8960054

brainly.com/question/4273177

#LearnwithBrainly

5 0
2 years ago
An element's atomic number is 34. How many protons would an atom of this element have?
Elena-2011 [213]

34. The element would have 34 protons. Also 34 electrons.

7 0
2 years ago
Other questions:
  • What happens to the electronegativity of elements as you move from bottom left to upper right across the periodic table?
    13·1 answer
  • A 1.50-kg iron horseshoe initially at 550°C is dropped into a bucket containing 25.0 kg of water at 20.0°C. What is the final te
    11·2 answers
  • You have a radioactive sample with a half-life of 1 hour. At t = 1 hour, a Geiger counter measures its radiation at 40 counts/mi
    6·1 answer
  • This is a textbook question, work too please!
    15·1 answer
  • A heat engine has a maximum possible efficiency of 0.780. If it operates between a deep lake with a constant temperature of-24.8
    13·1 answer
  • Curious George is whirling a 2.0 kg bunch of bananas on a smooth floor in a circular path having a radius of 0.50 m. What force
    9·1 answer
  • PLEASE HELP!!<br> What is osteoporosis? What are the symptoms and treatments?
    5·2 answers
  • Arrange the objects in order from greatst to least of potential energy assume that gravity is constant
    15·1 answer
  • 4. In which of the following circuits will the bulb glow?
    8·1 answer
  • The van accelerates at 2.2m/s^2. The force causing the acceleration is 5.5 kN. Calculate the mass of the van
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!