Solve Harmonic Oscillation Homework: E, F, T, ƒ

In summary, The problem is asking for the maximum force on an object during an oscillation, and trying to find the equation for that force. The problem also asks for the energy stored in a spring when it is compressed over a distance, and trying to find the expression for the restoring force.
  • #1
MisterP
47
3

Homework Statement


Harmonically fluctuating object. It`s full energy (E) is 3*10-5 J. Maximum force (F) on object is 1.5 * 10-3N. Period is 2 seconds (T) and starting phase (ƒ) is 60°. Need to write equation for these fluctuations.
E = 3*10-5 J
F= 1.5 * 10-3N
T = 2 s
ƒ = 60°

Homework Equations


I know this formula X (fluctuation formula) = A*cos(ω*t + ƒ)
ω - fluctuation angular frequency
t - time
ƒ - starting phase

The Attempt at a Solution


I found this formula E/F = A/2. Looks like I can calculate A (max amplitude). So 3*10-2/1.5 * 10-3 = A/2 A = 0.04 m (I guess it is in meters?)
So, how can I calculate ω now? Edit: just found ω = 2Π/t, could this be right?
 
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  • #2
MisterP said:
I found this formula E/F = A/2.
Unless you were told you could use such an equation, my guess is that you need to derive that from more fundamental principles.

MisterP said:
A = 0.04 m (I guess it is in meters?)
Don't guess, derive it.

MisterP said:
So, how can I calculate ω now? Edit: just found ω = 2Π/t, could this be right?
Do you think this makes sense? What is the definition of the period of oscillation.
 
  • #3
Hi again P,

You work in a telegraph office ? Such a terse problem statement :wink: !
 
  • #4
BvU said:
Hi again P,

You work in a telegraph office ? Such a terse problem statement :wink: !
I think that the problem was not originally in English.

By the way, @MisterP, I have changed the title of the thread. These are "oscillations" in English, not "fluctuations."
 
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  • #5
Seems like a tricky task to me, so I see this so "foggy"
English is not my original language, so its hard to translate such tasks :D :)
 
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  • #6
Still can`t figure this out..
 
  • #7
MisterP said:
Maximum force (F) on object is 1.5 * 10-3N
At what point in the oscillation period is the restoring force maximum ?
MisterP said:
It`s full energy (E) is 3*10-5 J
What is the energy stored in a spring with spring constant ##k## when it is compressed over a distance ##x## ?
What is the expression for the restoring force exercised by a spring with spring constant ##k## when it is compressed over a distance ##x## ?

Animated-mass-spring.gif

picture: wikipedia "oscillation" (lemma has no useful formulas for this exercise)
 

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Related to Solve Harmonic Oscillation Homework: E, F, T, ƒ

What is harmonic oscillation?

Harmonic oscillation is a type of periodic motion in which the restoring force is directly proportional to the displacement from the equilibrium position. It is characterized by a sinusoidal wave in which the system repeats the same motion over and over again.

What are the key components of solving harmonic oscillation homework?

The key components of solving harmonic oscillation homework are understanding the concepts of energy, force, time, and frequency. These components are used to analyze and describe the motion of harmonic oscillators.

How do I calculate the energy of a harmonic oscillator?

The energy of a harmonic oscillator can be calculated using the formula E = 1/2 * k * A^2, where k is the spring constant and A is the amplitude of the oscillation. The energy of a harmonic oscillator is constant and is split evenly between potential and kinetic energy.

What is the relationship between the period and frequency of a harmonic oscillator?

The period of a harmonic oscillator is the time it takes for one complete oscillation, while the frequency is the number of oscillations per unit time. The relationship between the two is that period (T) is equal to 1/frequency (ƒ), or T = 1/ƒ.

How can I use the fundamental frequency to analyze a harmonic oscillator?

The fundamental frequency, also known as the natural frequency, is the frequency at which a harmonic oscillator will oscillate with the greatest amplitude. It can be used to analyze a harmonic oscillator by finding its value and using it to determine the frequency and period of oscillation.

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