# Homework Help: Harmonic Motion Spring Constant

1. Jun 4, 2014

### 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!

1. The problem statement, all variables and given/known data
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.

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

3. 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

2. Jun 4, 2014

### ehild

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

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

ehild

3. Jun 5, 2014

### 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

4. Jun 5, 2014

### 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

5. Jun 5, 2014

### 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?

6. Jun 5, 2014

### Rookie

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

Last edited: Jun 5, 2014
7. Jun 5, 2014

### Rookie

ω = 2 * 3.1415 / 4 (T)
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 =)

8. Jun 5, 2014

ω2=k/m

ehild

9. Jun 5, 2014

### Rookie

Okay hows this?
ω² = (F/s)/m
ω² =k/m

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

10. Jun 5, 2014

### ehild

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

ehild