# Homework Help: Mass-Spring System Equation

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1. Sep 26, 2016

• Thread moved from General Physics, thus no formatting template is shown.
A mass-spring system is in free vibration after an initial excitation. There are no outside forces acting on the system. What is the value of the spring stiffness k (units of N/m; round your answer to a single decimal place)?

Mass m = 0.6 kg
Amplitude A = 0.4

Using this equation:
z(t) = A sin (w0 t)

Where w0 = SQUARE ROOT k/m
k is in the unit N/m and m is in the unit kg

2. Sep 26, 2016

### Hesch

You must know ω0.

The value of A doesn't matter.

3. Sep 26, 2016

Okay, but I need help figuring out the value of ω0!
I know the value of m (0.6 kg), so I just need to figure out k!
Do you know how to figure that out?

4. Sep 26, 2016

### Staff: Mentor

You cannot determine ωo or k from the given information. Is the question statement word-for-word complete?

5. Sep 26, 2016

Yes, that's the entire question. There is also a graph if that helps at all.

6. Sep 26, 2016

### Staff: Mentor

The graph is key to the problem. What information can you glean from the graph?

7. Sep 26, 2016

Amplitude, frequency, and period.
Is frequency equal to ω0?
And frequency I believe would be 3, correct?

8. Sep 26, 2016

### Staff: Mentor

Period T (Seconds) and frequency f (Hz) are both related to angular frequency ω (radians / sec). Do you know the relationships between these quantities? It comes up a lot so it's worth committing to memory.

9. Sep 26, 2016

Angular frequency is equal to 2πf, if I remember correctly. So since f=3 in this example, would angular frequency be equal to 6π?

10. Sep 26, 2016

### Staff: Mentor

Yes, but be sure to always include units when you quote values. In most cases in physics (and all sciences) a number alone is meaningless.

So f = 3 Hz and ω = 6π rad/sec.

11. Sep 26, 2016

Okay, that works out! Thank you so much for your help!!

12. Sep 26, 2016

### Staff: Mentor

You're welcome. Good luck with your studies.