Veriticle springs; period and mass?

[wow22]

Homework Statement

Information provided is: mass of spring, displacement, force of constant, gravity.
so basically: m, x, k, and g
Determine the relationship between the period and mass

so how do i find T?

Homework Equations

T= seconds/cycles
T= 2π(sqrt(m/k))

The Attempt at a Solution

I used T= seconds/cycles and got 0.47
BUT. when i used 2π(sqrt(m/k)) I got 0.39

shouldnt both formulas be right?
why are my answers different?
Thanks!

 

[tiny-tim]

sho

hi wow22!

I used T= seconds/cycles and got 0.47
BUT. when i used 2π(sqrt(m/k)) I got 0.39

show us your full calculations, and then we'll see what went wrong

 

[wow22]

m=100g = 0.1kg
g= 9.8 m/s^2
k= 26.6

so when
2π(sqrt(m/k))
=2π(sqrt(0.1/26.6))
0.39

seconds/cycles
t=4.7s
cycles=10

so
t/cycles= 4.7s/10
=0.47
.. :s

 

[tiny-tim]

where do 10 and 4.07 come from?

and what is this spring doing?

 

[wow22]

We calculated the time it takes for the hanging mass attached to the spring To fall and make 10 cycles . So tits 10 cycles in 4.7s

 

[tiny-tim]

We calculated …

you mean you measured it?

then some of your other data must be wrong

 

[wow22]

Yeah... But we double checked with other groups and it was relatively the same .. But ideally, If I had the correct information, should both of finding period work ? :S

 

[tiny-tim]

But ideally, If I had the correct information, should both of finding period work ? :S

yes of course!

probably the k they gave you was wrong

 

[wow22]

Oh actually we had to find k too :S

But thanks again tiny-tim :D

 

[wow22]

Can someone just check if these are correct:

the amplitude does not affect the period of vibration within a spring because the period will only change if the mass or force constant changes.

a mass experiences dynamic equilibrium when the mass is hanging on the spring at its most stretched/compressed displacement (so when v=0m/s)

a mass experiences its maximum speed when it is in the middle of its stretched displacement

the acceleration of the mass is constant because the only acceleration acting on the mass is gravity

(this does the same thing with the verticle spring stuff up there^)

 

[tiny-tim]

the amplitude does not affect the period of vibration within a spring because the period will only change if the mass or force constant changes.
…
a mass experiences its maximum speed when it is in the middle of its stretched displacement

yes

a mass experiences dynamic equilibrium when the mass is hanging on the spring at its most stretched/compressed displacement (so when v=0m/s)

i know what you mean (and it's correct), but that's not called dynamic equilibrium

dynamic equilibrium has to be equilibrium, ie balanced forces (see http://en.wikipedia.org/wiki/Dynamic_equilibrium), and this isn't

the acceleration of the mass is constant because the only acceleration acting on the mass is gravity

sorry, this is nonsense

acceleration does not act, it just is

one body has only one acceleration

there are two forces on the body … one is constant (gravity), the other isn't

the acceleration is certainly not constant, it's harmonic, and proportional to the displacement

 

[MrWarlock616]

@tiny-tim : how? the maximum velocity is at the mean position. So even if it is at the midpoint of stretched displacement, it does not have max velocity. So I think second one is wrong, isn't it?

 

[tiny-tim]

… mean position … midpoint of stretched displacement

they're the same, aren't they?

it's simple harmonic motion, so the maximum speed is at the midpoint

 

[MrWarlock616]

they're the same, aren't they?

oh yeah i got it now thanks :) i thought midpoint was amplitude/2

 

[wow22]

:$ Sorry I'm kind of lost..
So when IS it in dynamic equilibrium? it's supposed to be when the two forces acting on it are equal no? so gravity=force of tension i was geussing..

Thanks!

 

[tiny-tim]

So when IS it in dynamic equilibrium?

i wouldn't apply it to this case, since the system is continually changing, but if you did, it would be when the forces are balanced, and the system isn't changing

for example, there's dynamic equilibrium for the water-air mixture in a sealed container: water molecules are continually leaving the liquid water (evaporating) and joining the air, while other water molecules are leaving the air and joining the liquid water …

overall, the proportion of water in the air stays the same, so there's equilibrium, but since the actual molecules are dodging to and fro, the equilibrium is dynamic​

 

[wow22]

Okay thanks! Well our lab asks us when it is in dynamic equilibrium :S do I should write that there is home?

 

[tiny-tim]

Okay thanks! Well our lab asks us when it is in dynamic equilibrium :S do I should write that there is home?

i've no idea

what has your professor given you as the definition of dynamic equilibrium?

 

[wow22]

when forces are balanced, the mass will move at a constant velocity.

 

[tiny-tim]

when forces are balanced, the mass will move at a constant velocity.

but there's no constant velocity here

(unless either

i] we regard the velocity at any point as instantaneously constant, or

ii] it means that the magnitude of the velocity is instantaneously at a maximum or minimum)​