Value of Spring Stiffness k in Free Vibration of Mass-Spring System

[Canada95]

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

 

[Hesch]

What is the value of the spring stiffness k (units of N/m; round your answer to a single decimal place)?

You must know ω₀.

The value of A doesn't matter.

 

[Canada95]

You must know ω₀.

The value of A doesn't matter.

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?

 

[gneill]

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

 

[Canada95]

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

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

 

[gneill]

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

 

[Canada95]

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

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

 

[gneill]

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

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.

 

[Canada95]

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.

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

 

[gneill]

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

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.

 

[Canada95]

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.

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

 

[gneill]

You're welcome. Good luck with your studies.