Solve Oscillation Problems: Find Mass m with Frequency Change

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In summary, the conversation discussed finding the value of mass m in a spring oscillation problem based on given frequencies and an added mass. The solution involved finding the angular frequencies and setting up and solving a ratio equation to find the value of m.
  • #1
Shackleford
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Homework Statement



A mass m at the end of a spring oscillates with a frequency of 0.83 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of me?

Homework Equations



w = 2 pi f

w^2 = k / m

The Attempt at a Solution



m = .74725 kg

I'll probably be adding a few more problems, as my textbook didn't come with a solutions manual. I wish it did.
 
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  • #2
Hmm.. I got 0.744kg.

Did you find w first and then sub it in with a rounded off value?

Or did you find m algebraically and then evaluate?
 
  • #3
jaseh86 said:
Hmm.. I got 0.744kg.

Did you find w first and then sub it in with a rounded off value?

Or did you find m algebraically and then evaluate?

Our answers are close enough. It looks like I did it correctly.

I found the two "w"s first, expressed the masses in terms of m, setup a ratio and solved for m.
 

What is oscillation and how does it relate to mass and frequency?

Oscillation is the repetitive back and forth motion of an object. The mass and frequency of an object are directly related to its oscillation. An increase in mass will result in a decrease in frequency, while a decrease in mass will result in an increase in frequency.

Why is it important to solve oscillation problems and find mass with frequency change?

Solving oscillation problems and finding mass with frequency change is important because it helps us understand the behavior of oscillating systems, such as pendulums and springs. It also allows us to make predictions and calculations for these systems, which are essential in fields such as engineering and physics.

What is the formula for finding mass with frequency change in an oscillating system?

The formula for finding mass with frequency change is m = (4π^2k)/ω^2, where m is the mass, k is the spring constant, and ω is the angular frequency. This formula is derived from Hooke's Law and the equation for angular frequency, ω = 2πf, where f is the frequency in hertz.

What are some common real-life examples of oscillating systems?

Some common real-life examples of oscillating systems include pendulums, diving boards, and guitar strings. Other examples include the motion of a swing, a bouncing ball, and a mass attached to a spring.

What are some tips for solving oscillation problems and finding mass with frequency change?

Here are some tips for solving oscillation problems and finding mass with frequency change:

  • Identify the known values, such as the spring constant, frequency, and mass.
  • Use the formula m = (4π^2k)/ω^2 to calculate the mass.
  • Make sure to convert units to match the formula (e.g. converting from seconds to hertz for frequency).
  • Check your answer by plugging it back into the original equation and making sure it satisfies the given conditions.

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