Harmonic Motion Spring Constant

[Rookie]

Hello I was given this problem, and I have two possible answers and I really just need someone to verify which one is right, or at least in the right direction. Thanks!

Homework Statement

A cart is floating on an airtrack and is connected by a spring to one fixed object. The cart executes simple harmonic motion with a period of 4 seconds. Its mass is 2kg. Its maximum displacement from rest position is 1.8m. Calculate the spring constant and provide units.

Homework Equations

Given in problem statement:
ω² = (F/s)/m
What I found online:
k = -F/x

The Attempt at a Solution

Using k = -F/x ( But I'm not sure I was suppose to use this equation.
k = - F(force=ma)/x(displacement)
k = - 2*9.8/1.8
k= - 196/1.8
k= 108.89 n/m

Using ω² = (F/s)/m I came up with
ω² = (F/s)/m
(196/4)/2 = 24.5 n/m

 

[ehild]

Hello I was given this problem, and I have two possible answers and I really just need someone to verify which one is right, or at least in the right direction. Thanks!

Homework Statement

A cart is floating on an airtrack and is connected by a spring to one fixed object. The cart executes simple harmonic motion with a period of 4 seconds. Its mass is 2kg. Its maximum displacement from rest position is 1.8m. Calculate the spring constant and provide units.

Homework Equations

Given in problem statement:
ω² = (F/s)/m
What I found online:
k = -F/x

The Attempt at a Solution

Using k = -F/x ( But I'm not sure I was suppose to use this equation.
k = - F(force=ma)/x(displacement)
k = - 2*9.8/1.8

How does the gravitational acceleration come in? The cart is on an air-track, and floats. It does not fall!

Using ω² = (F/s)/m I came up with
ω² = (F/s)/m
(196/4)/2 = 24.5 n/m

You have to know the meaning of the symbols in the formula you are using. What are F, s, ω?

ehild

 

[Rookie]

F = force
s = Seconds
omega is angular velocity
I pretty sure those are right, not sure about s though.

And about the gravitational acceleration, I guess that was a mistake haha

 

[ehild]

You used mg = 196 N for the force. It is wrong.
Read about SHM (simple harmonic motion) in your book or lecture notes. What force acts to objects performing SHM? How is ω related with the spring constant (k) and the mass (m)?

ehild

 

[Rookie]

okay so ω is angular frequency, s was displacement.
ω = spring constant (k) / mass (m)
So if I want the spring constant I would need to work out ω and then ω * m which would equal the spring constant?

 

[Rookie]

ω also equals 2π/f, 2 * pi / T
frequency = 1/T

 

[Rookie]

ω = 2 * 3.1415 / 4 (T)
ω = 1.57 rad/s
k = ω * m
k = (3.14²) * 2

k = 6.28 n/m
Okay I think that this is the answer! Please check what I've done =)

 

[ehild]

okay so ω is angular frequency, s was displacement.
[STRIKE]ω = spring constant (k) / mass (m)[/STRIKE]
So if I want the spring constant I would need to work out ω and then ω * m which would equal the spring constant?

ω²=k/m

ehild

 

[Rookie]

Okay hows this?
ω² = (F/s)/m
ω² =k/m

ω = 2π/T
ω = 2 * 3.1415 / 4 (T)
ω = 1.57 rad/s
ω convert to ω²
ω² = 2.46
k = ω² * m
k = 2.46 * 2
k = 4.93 n/m

 

[ehild]

It is much better. But "Newton", the unit of force, is abbreviated with capital N.

ehild