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
OleMash [197]
3 years ago
11

A light platform is suspended from the ceiling by a spring. A student with a mass of 90 kg climbs onto the platform. When it sto

ps bouncing and reaches its new equilibrium position (x=0), the student notices that the spring has stretched 0.82 m. The student's friend pulls the platform down 0.32 m further and then releases it at t=0. What is the amplitude of the motion of the student on the platform?

Physics
1 answer:
Ilya [14]3 years ago
6 0
Refer to the diagram shown.

When the student climbs onto the platform, the spring stretches by 0.82 m to reach the equilibrium position.
The mass of the student is m = 90 kg, so his weight is
mg = (90 kg)*(9.8 m/s²) = 882 N

By definition, the spring constant is
k = (882 N)/(0.82 m) = 1075.6 N/m

When the spring is stretched by x from the equilibrium position, the restoring force is
F = - k*x.

If damping is ignored, the equation of motion is
F = m * acceleration
or
m \frac{d^{2}x}{dt^{2}} = -kx \\ \frac{d^{2}x}{dt^{2}} + \frac{k}{m} x = 0

Define ω² = k/m = 11.751 => ω = 3.457.
Then the solution of the ODE is
x(t) = c₁ cos(ωt) + c₂ sin(ωt)

x'(t) = -c₁ω sin(ωwt) + c₂ω cos(ωt)
When t=0, x' =0, therefore c₂ = 0

The solution is of the form
x(t) = c₁ cos(ωt)
When t = 0, x = 0.32 m. Therefore c₁ = 0.32

The motion is
x(t) = 0.32 cos(3.457t)
The single amplitude is 0.32 m, and the double amplitude is 0.64 m.

Answer: 
0.32 m (single amplitude), or
0.64 m (double amplitude)

You might be interested in
Which are considered noble gases
sladkih [1.3K]

Answer:Argon

Neon

Helium

Krypton

Xenon

4 0
2 years ago
Read 2 more answers
Block A with mass mA=4.6 kg lies on a frictionless incline plane. It is connected by a massless rope over a frictionless, massle
lara31 [8.8K]

Answer:

Check the explanation

Explanation:

In calculate kinetic energy, write out a formula whereby the kinetic energy will be equal to 0.5 times mass times velocity squared. include in the value for the object mass, then the velocity with which it is moving.

Kindly check the attached image below to get the step by step explanation to the question above.

8 0
3 years ago
Referring to the map of the temperature field in the room, where was the warmest field found?
klasskru [66]
Is there supposed to be an image if so there is none
8 0
3 years ago
Read 2 more answers
Are plants carnivores<br>Ture or False​
monitta

Answer:

False they are producers and they don' eat anything only produce and provide

Explanation:

3 0
3 years ago
Describe a situation when you might travel at a high velocity bit with low acceleration
iren [92.7K]

I am sitting in my seat.
I am listening to my mp3 and reading my book.
My eyes are getting heavy.  They start to close.
I try to stay awake, but it's no use.
I am so warm and comfortable and sleepy,
and I have just finished my dinner.
Finally I can't help it.  Resistance is futile.
I give up, and fall deep asleep.
My head rests back against my soft, comfy seat.

My seat is in row 26 on the airplane I'm flying in
to visit my grandmother on the coast.
We are cruising at 560 miles an hour, bearing 280°,
at flight level 320 .
The temperature outside my window is  -60°F .

5 0
3 years ago
Other questions:
  • Look at the circuit diagram.
    6·2 answers
  • Determine the minimum angle at which a frictionless road should be banked so that a car traveling at 20.0 m/s can safely negotia
    14·1 answer
  • Which following is step two of the five step worksheet creation process
    6·1 answer
  • Which quantity is a vector quantity A. Acceleration B. Mass C. Speed D. Volume
    10·1 answer
  • NASA developed a reflective foil barrier to help shield spacecraft from heat transfer in space. These reflective barriers are no
    13·1 answer
  • You are trying to gain possession of the soccer ball. What position are you playing?
    7·1 answer
  • A group of students left school at 8:00 am on a field trip to a science museum 90 miles away. Which best describes the average s
    13·1 answer
  • If a person wanted to engineer a new type of communication device, what field of study would be the most useful?
    9·1 answer
  • Choose one inner planet and one outer planet and compare their similarities and differences.
    11·2 answers
  • How much work does a football player do in the weight room when he squats 150 kg up a distance of 1 meter?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!