I need help with this math problem?

Question

a)A spring with a 4 kg mass has natural length 1 m and is maintained stretched to a length of 1.3 m by a force of 24.3 N. If the spring is compressed to a length of 0.8 m and then released with zero velocity, find the position of the mass at any time t
b)A spring with a 3 kg has damping constant 30 and spring constant 123. x(t)=?
(a) Find the position of the mass at time t if it starts at the equilibrium position with a velocity of 2 m/s. x(t)=?

i know it's physics..but i'm taking it in my calculus 2 class..that's why i posted it here..

Answer 1

this isn't math, it is physics so try posting it in the physics forum for physics people to help you with it.

ELASTIC POTENTIAL ENERGY
When a person jumps from the top of a crane, they immediately reduce their height
and gravitational potential energy. Where does the energy go? Obviously, the
potential energy becomes kinetic (motion) energy. But where is the energy when
you come to a stop just before impacting the ground?
A bungee cord is a giant spring (elastics, guitar strings, bow strings, etc are all
springs) and it holds the energy as elastic potential energy.
Springs exhibit simple harmonic motion. That is to say that they vibrate back and
forth or up and down with a regular period. Also, a restoring force acts to move the
spring back to its equilibrium position and the size of this force is proportional to the
displacement from equilibrium. This is Hooke's Law:
F = kx where:
k = spring constant (N/m)
x = displacement from equilibrium position (m)
In Newtonian mechanics, if W = Fd , then for a spring W = Fx. Because the
amount of force is proportional to the displacement, F is an average force.
Therefore, W = 1/2Fx which must mean that Ep = 1/2 Fx.
Combining two formulas will give an energy equation that can be used to solve elastic problems.
If F = kx and Ep = 1/2Fx then Ep = 1/2(kx)x which means Ep = 1/2 kx2
The force of gravity and the elastic force of an ideal spring or bow are referred to as conservative forces. A conservative
force is a force that, when work is done against it, this work is stored and is recoverable. You see, if work is done
against gravity, this work is stored and can be recovered at some later time.
For example, if a pile driver is lifted to a certain height -- work is done against gravity on the pile
driver -- the pile driver now has potential energy. When the pile driver is dropped on a pile, work
is done on the pile by the pile driver.
The photo to the right shows a pile driver (long, heavy pipe) which is dropped on piling or
support structures in the ground, beneath the water.
Similarly, if a force is exerted on a spring to compress it, work is done against the spring. Now,
this spring can be used to project an object -- that is, work was done on the spring. The spring
now has potential energy. When the spring is released, work is done on the object by the spring.
Workbook – Energy Conservation 6 of 12
Friction is a non-conservative force. Work done against friction cannot be recovered. Work done against friction is
converted into some other form of energy -mainly thermal energy.
POTENTIAL ENERGY SUMMARY
Definition:
Definition: Energy due to position, or stored energy.
Formula: Ep = mgh (gravitational) Ep = 1/2kx2 (elastic)
Unit: Joule (J)
KINETIC ENERGY

being launched on a mag-lev rail.
When a rocket is launched, a force is applied and this force acts through some
distance; therefore, work is done. However, when the object is released, it has a
speed; it has kinetic energy. Kinetic energy is energy of motion. The work "kinetic"
comes from the language for the word "motion". The work done in accelerating this
object from rest becomes kinetic energy. Kinetic energy is calculated using:
Ek = 1/2mv2
KINETIC ENERGY SUMMARY
Definition:
Definition: Energy of motion
Formula: Ek = 1/2mv2
Unit: Joule (J)
Example Problem: Superman jumps from a 150 m high building. If he has a mass of 65.3 kg (including his spandex
tights), how much gravitational potential energy does he have?
p
2
p
4
p
Ep= mgh
Ep= (65.3 kg)(9.81 m/s )(150 m)
Ep= 9.61 10 J

Example Problem: A bungee cord has a spring constant of 5.00 N/m. If a three legged monkey stretches the cord
35.2 m from equilibrium position, how much potential energy is in the spring?
Ep= 1/2kx
Ep= 1/2(5.00 N/m)(35.2 m)
Ep= 3.10 10J

Example Problem: The batmobile is travelling at 35.0 km/h and has a kinetic energy of 4.00 x 104 J. What is the
batmobile’s mass?

35.0 km 1000 m 1 h 9.72 m/s
h km 3600 s
Ek= 1/2mv2
2E/v=m= 2(40000J)
/9.72 m/s^2=423kg

Answer 2

As its almost impossible to just give you the equations on Yahoo Answers, so I suggest you trying looking in your Physics notes rather than your Math Notes. It's a fairly simple problem if you just pick it apart. Review your spring equations and it will probably require you to do an integral or differential equation to obtain your position. If you are still stuck, I suggest you go speak to your teacher/professor. They can probably get you going in the right direction.

Answer 3

aw man you want us to solve a differential equation for you? it's friday night and i just ran out of beer.

But hold on tight, the science brigade will be right along; they've helped me out of many a tight spot and never disappoint....

all i remember is that the first bit will be something like

x = A.cos(omega.t)

and when you add the damping in it will look more like

x = A.exp(B.t).cos(omega.t)

and if you're going to put a velocity boundary condition on, you're gonna have to differentiate that to get dx/dt (velocity) before you do.

Right, there are dishest to wash; i'm off

Answer 4

The mass of a spring is not going to change, no matter how much you squeeze or stretch it.

Answer 5

3. 80x 4. 80x + a million 5. 250(80x + a million) 6. 250(80x + a million) + y 7. 250(80x + a million) + 2y 8. 250(80x + a million) + 2y - 250 9. [250(80x + a million) + 2y - 250] / 2 = [20000x + 250 + 2y - 250] / 2 = [20000x + 2y] / 2 = 10000x + y

Answer 6

Your best bet would be to go to www.algebra.com. You can click on your math class (ie. algebra, geometry, calculus...) and then you can ask a professional tutor. They will get back to you within 24 hours. Hope this helps.

Answer 7

hah, that sounds like vibrations homework to me. but i dun have my vibrations book rite now... so can't help you sorry >=P but maybe you should draw a diagram of it and just look in your book which situation fits it best, its probably really easy to relate this particular problem to a given example. ps you mite want to post this in the engineering section to get a better answer.

Answer 8

What school are you going to? I love math problems but I don't have time to help you right now. I'll check back tomorrow to see how it's going. xxx

Answer 9

arrrr NOT MATHS.............i just finished maths for like the whole of my life...although im good at it lol i would love to help but ive sort of forgotten everything about it

Answer 10

This is going to cost you!