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
Lerok [7]
3 years ago
8

A mass of 3.25 kg is attached to the end of a spring that is stretched 22 cm by a force of 15 N. It is set in motion with an ini

tial position x0=0 and initial velocity (in m/s) v0=−12. Find the amplitude, period, and frequency of the resulting motion. You should assume that the system is frictionless.
Mathematics
1 answer:
mylen [45]3 years ago
5 0

Answer:

Step-by-step explanation:

Given that,

Mass of object=3.25kg

The extension e=22cm=0.22m

Force applied to cause extension F=15N

Initial position Xo=0

Initial velocity Vo=-12m/s

We can get the spring constant from Hooke's law

F=ke

Then, k=F/e

k=15/0.22

k=68.182N/m

Also our natural frequency w is given as

w=√(k/m)

Therefore,

w=√(68.182/3.24)

w=√20.98

w=√21

w=4.58rad/s

w=4.6rad/s

There is no damping in this situation, no outside force acting on the system and the equation that governs the system is

mx''+kx=0

3.25x''+68.182x=0

Divide through by 3.25

x''+20.98x=0

We can approximate 20.98 to 21

x"+21x=0

The solution to this differential equation using D operator

D²+21=0

D²=-21

D= ±√-21

D=±√21 •i

Then the solution is

x(t)=A•Sinwt +B•Coswt

x(t)=A•Sin√21 t +B•Cos√21 t

Note that x'(t)=v(t)

and at t=0 Vo=-12m/s

x(t)=A•Sin√21 t +B•Cos√21 t

x'(t)=v(t)=A√21•Cos√21 t - B√21•Sin√21 t

v(t)=A√21•Cos√21 t - B√21•Sin√21 t

Then, using the two initial conditions

v(0)=-12

And X(0)=0

x(t)=A•Sin√21 t +B•Cos√21 t

X(0)=A•Sin√21•0 +B•Cos√21•0

X(0)=A•Sin0+B•Cos0

0=B

B=0

Also,, V(0)=-12m/s

v(t)=A√21•Cos√21 t - B√21•Sin√21 t

V(0)=A√21•Cos√21•0- B√21•Sin√21•0

V(0)=A√21•Cos0- B√21•Sin0

-12=A√21

Therefore,

A=-12/√21

A=-2.62

Therefore the general equation becomes

x(t)=A•Sin√21 t +B•Cos√21 t

x(t)=-2.62Sin√21 t +0•Cos√21 t

x(t)=-2.62Sin√21 t

a. The amplitude

Comparing x(t) to wave equations

x(t)=-Asin(wt+2λ/t)

Then,

A=2.62m

b. We know the natural frequency already to be

w=√21

w=4.58rad/s

c. Period

Comparing the equation again

wt=√21t

Given that w=2πf

Therefore, 2πft=√21t

Then, f=√21t / 2πt

f=√21/2π

f=0.73Hz

Then, period is the reciprocal of frequency

T=1/f

T=1/0.73

T=1.37seconds

The period is 1.37sec,

You might be interested in
Graph from slope intercept form y=-1/3x+5
jolli1 [7]

Answer:

Attached image.

Slope = -1/3

y-intercept = (0,5)

8 0
2 years ago
Complete the table and then graph the function.
Gekata [30.6K]

Answer:

You plug in x and solve for each value. Look at attachment for answers

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
lung cancer kills about 3,000 people per day. if 90% of the deaths from luung cancer are attributted to smoking, what is the rat
defon

Answer:

2700!

Step-by-step explanation:

hope that helped <3

5 0
3 years ago
Rob is cooking a cake.The recipe calls for 9 cups of flour.He has already put in 3 cups. How many more cups does he need to put
svetoff [14.1K]

Answer:

9-3= 6 Cups

Step-by-step explanation:

Recipe needs 9 cups of flour, Rob has added 3 cups already so he needs to add 6 more cups to make it 9 cups.

7 0
2 years ago
ASAP PLZZZZZZZ ANSWER RIGHT
Darina [25.2K]

Answer: ALZ is congruent to AIR by reason ASA

Step by Step Explanation:  i hate rsm

8 0
3 years ago
Other questions:
  • Martin wants to plot a graph to show the prices of different numbers of helmets. He has to plot the following points: (1, 24.97)
    8·2 answers
  • If 1 yard = 3 feet and 1 mile = 5,280 feet, how many yards are there in 2 miles? 2,640 yards 3,520 yards 10,560 yards 31,680 yar
    8·1 answer
  • The perimeter of the rectangle is 48 feet. The length is 16 ft. What is the<br> width?
    12·1 answer
  • Break apart 54 to solve 54 diveded into 6
    10·1 answer
  • Tony believes that the more time he spends at the record store, the more money he tends to spend. To see if he is correct, he ke
    13·1 answer
  • Help!??? I don’t understand!!!!
    6·1 answer
  • What happens if I have $84 in 1/4 is taken away how manny do I have left
    14·1 answer
  • Number 9 on my integrated geometry test
    5·1 answer
  • A map of a city uses a scale of 1cm =3.5 meters. If a road shown on the maps runs for 25cm how long is the road?
    10·2 answers
  • People are randomly chosen from a group of 7 boys and 5 girls. Determine which scenario is more likely to happen.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!