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
Alekssandra [29.7K]
3 years ago
11

A mass of 1 g is set in motion from its equilibrium position with an initial velocity of 6in/sec, with no damping and a spring c

onstant of k = 9. Find (a) the solution y for the displacement of the spring, (b) the time when the mass first returns to equilibrium (i.e. displacement y = 0), (c) it's velocity at the time you found in (b). slader
Mathematics
1 answer:
yan [13]3 years ago
4 0

a) y(t)=0.0016 sin(94.9t) [m]

b) 0.033 s

c) -0.152 m/s

Step-by-step explanation:

a)

The force acting on the mass-spring system is (restoring force)

F=-ky

where

k = 9 is the spring constant

y is the displacement

Also, from Newton's second law of motion, we know that

F=my''

where

m = 1 g = 0.001 kg is the mass

y'' is the acceleration

Combining the two equations,

my''=-ky

This is a second order differential equation; the solution for y(t) is

y(t)=A sin(\omega t-\phi)

where

A is the amplitude of motion

\omega=\sqrt{\frac{k}{m}}=\sqrt{\frac{9}{0.001}}=94.9 rad/s is the angular frequency

The spring starts its motion from its equilibrium position, this means that y=0 when t=0; therefore, the phase shift must be

\phi=0

So the displacement is

y(t)=A sin(\omega t)

The velocity of the spring is equal to the derivative of the displacement:

v(t)=y'(t)=\omega A cos(\omega t)

We know that at t = 0, the initial velocity is 6 in/s; since 1 in = 2.54 cm = 0.0254 m,

v_0=6(0.0254)=0.152 m/s

And since at t = 0, cos(\omega t)=1

Then we have:

v_0=\omega A

From which we find the amplitude:

A=\frac{v_0}{\omega}=\frac{0.152}{94.9}=0.0016 m

So the solution for the displacement is

y(t)=0.0016 sin(94.9t) [m]

b)

Here we want to find the time t at which the mass returns to equilibrium, so the time t at which

y=0

This means that

sin(\omega t)=0

We know already that the first time at which this occurs is

t = 0

Which is the beginning of the motion.

The next occurence of y = 0 is instead when

\omega t = \pi

which means:

t=\frac{\pi}{\omega}=\frac{\pi}{94.9}=0.033 s

c)

As said in part a), the velocity of the mass-spring system at time t is given by the derivative of the displacement, so

v(t)=\omega A cos(\omega t)

where we have

\omega=94.9 rad/s is the angular frequency

A=0.0016 m is the amplitude of motion

t is the time

Here we want to find the velocity of the mass when the time is that calculated in part b):

t = 0.033 s

Substituting into the equation, we find:

v(0.033)=(94.9)(0.0016)cos(94.9\cdot 0.033)=-0.152 m/s

You might be interested in
Need help solving for X
Stels [109]
I hope this helps you



x=108/6


x=18

4 0
3 years ago
What’s the value of x?<br><br> What’s the angle measures
slava [35]
7 I just took the test! Hope this helped
4 0
2 years ago
A rectangle length is 8cm more than three times it’s widith. The perimeter is 128 cm find the length.
Masteriza [31]
Let x = width
<span>length is 8 cm more than three times it’s width so length = 3x + 8
</span>
Perimeter of a rectangle = 2(L + W)
so
128 = 2(x + 3x + 8) solve for x (width)
128 = 2(4x + 8)
  64 = 4x + 8
  4x = 56
    x = 14
width = 14 cm
length = 3(14) + 8 = 50 cm

Answer:
width   = 14 cm
length  = 50 cm

4 0
3 years ago
What is 8×8=n×10 plz i need this​
spin [16.1K]

Answer:

n=32/5

Step-by-step explanation:

8 0
2 years ago
Write the statement in the if then form perpendicular lines intersect to form right angles
kvv77 [185]

Answer: If perpendicular lines intersect, then they form right angles.


Step-by-step explanation:

You take the first part, "perpendicular lines intersect", and add the "if" to it. Then, you take the second part, "to form right angles", and add the "then" in front of it to get your answer, "If perpendicular lines intersect, then they form right angles."

Hope it helps! :)

8 0
2 years ago
Other questions:
  • Jim has a home loan and a car loan. He defaults on his home loan after a year of making payments on time.However, he continues t
    10·2 answers
  • Identify the polynomial.
    9·1 answer
  • An experiment consists of rolling two fair number cubes. What is the probability that the sum of the two numbers will be 4? Expr
    10·1 answer
  • What is the reciprical for 73
    5·2 answers
  • I NEED HELP ASAP !!!!!!!!!!!!!!!!!!!!
    5·2 answers
  • Please please please help!! ASAP
    12·1 answer
  • The functions f(x) and g(x) are shown below:
    13·1 answer
  • This histogram represents a sampling of recent visitors to the mall on a Friday night, grouped by their ages.
    13·1 answer
  • Show your work plzz :))))
    6·2 answers
  • Solve this quetion...3
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!