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

In summary, the mass-spring system is in free vibration after an initial excitation. There are no outside forces acting on the system, so the value of the spring stiffness is unknown.
  • #1
Canada95
6
0
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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
 
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  • #2
Canada95 said:
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.
 
  • #3
Hesch said:
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?
 
  • #4
You cannot determine ωo or k from the given information. Is the question statement word-for-word complete?
 
  • #5
gneill said:
You cannot determine ωo 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.

Screen Shot 2016-09-26 at 9.41.09 PM.png
 
  • #6
The graph is key to the problem. What information can you glean from the graph?
 
  • #7
gneill said:
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?
 
  • #8
Canada95 said:
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.
 
  • #9
gneill said:
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?
 
  • #10
Canada95 said:
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.
 
  • #11
gneill said:
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!
 
  • #12
You're welcome. Good luck with your studies.
 

1. What is a Mass-Spring System Equation?

A Mass-Spring System Equation is a mathematical model that describes the motion of a mass attached to a spring. It takes into account the mass of the object, the spring constant, and any external forces acting on the system.

2. What are the components of a Mass-Spring System Equation?

The components of a Mass-Spring System Equation include the mass of the object (m), the spring constant (k), the displacement of the mass (x), and the acceleration of the mass (a). It can also include any external forces acting on the system, such as gravity or friction.

3. How is a Mass-Spring System Equation derived?

A Mass-Spring System Equation is derived using Newton's Second Law of Motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration. By applying this law to a mass attached to a spring, we can derive the equation for its motion.

4. What are the applications of Mass-Spring System Equation?

The Mass-Spring System Equation has many applications in physics and engineering. It is used to model the motion of objects such as car suspensions, buildings during earthquakes, and even the movement of molecules in a gas. It also helps to design and analyze systems that involve springs, such as shock absorbers and trampolines.

5. Are there any limitations to the Mass-Spring System Equation?

While the Mass-Spring System Equation is a useful model for many systems, it does have some limitations. It assumes that the spring is ideal and obeys Hooke's Law, which may not always be the case. It also does not take into account any external factors that may affect the system, such as air resistance or friction.

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