Please help asap classical mech( harmonic oscillator)

In summary, the conversation is discussing the mechanism powering a clock and how friction affects the amplitude of the harmonic oscillator used to keep time. The question posed is what the amplitude will be after 10 seconds if it is unity at t=0. There is mention of an equation involving angular frequency and hints are requested for solving the problem.
  • #1
belleamie
24
0
Please help
1) The mechanism which powers the clock (using a harmonic oscillator to keep time with friction) Since the clock has friction the oscillation amplitude decreases in time. If the oscillation amp is unity at t=0 what will the amp be after 10 sec?

I believe we need to use the equation w=sq rt(k/m-(c/2m)^2)
But I'm not exactly sure what is the correct way to arrpoach this problem, Any hint would be appreciated! thanks!
 
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  • #2
They're not asking (at this point) for the new *angular frequency*,
they're asking for the *envelope* of the decaying cosine curve.
x(t) will be A_o exp(-t/tau) cos(wt + phi) ; the question is about
the exp(-t/tau) portion. You need to know how strong friction is,
or how much frictional work is done in a cycle with total Energy E.
 
  • #3


I understand your urgency in seeking help with your classical mechanics problem involving a harmonic oscillator. To answer your question, we can use the equation you mentioned, w=sqrt(k/m-(c/2m)^2), where w represents the angular frequency of the oscillator, k is the spring constant, m is the mass of the oscillator, and c is the damping coefficient.

To find the amplitude after 10 seconds, we can use the equation for the displacement of a harmonic oscillator, x(t)=A*cos(wt+phi), where A is the amplitude and phi is the phase angle. Since the amplitude decreases in time due to friction, we can use the equation A=A0*e^(-ct/2m), where A0 is the initial amplitude at t=0.

Plugging in the values for w, k, m, and c, we can solve for the amplitude A after 10 seconds. However, please note that the phase angle phi is not given in the problem, so we cannot accurately determine the exact amplitude at t=10 seconds without knowing it.

I hope this helps guide you in solving your problem. It is always important to clearly state all known variables in a problem and use relevant equations to find the solution. If you need further assistance, please do not hesitate to reach out for help from a professor or tutor. Good luck!
 

1. What is a harmonic oscillator in classical mechanics?

A harmonic oscillator in classical mechanics refers to a system that exhibits a back-and-forth motion around an equilibrium point due to a restoring force. This type of oscillation follows a sinusoidal pattern and can be found in various physical systems, such as a mass attached to a spring or a pendulum.

2. How is the motion of a harmonic oscillator described mathematically?

The motion of a harmonic oscillator can be described using the equation of motion, which is a second-order differential equation. This equation takes into account the mass, spring constant, and displacement of the oscillator from its equilibrium position. The solution to this equation gives the position, velocity, and acceleration of the oscillator at any given time.

3. 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 the oscillator to complete one full cycle of its motion, while the frequency is the number of cycles per unit time. These two quantities are inversely related, meaning that as the period increases, the frequency decreases, and vice versa.

4. How does the amplitude affect the motion of a harmonic oscillator?

The amplitude of a harmonic oscillator refers to the maximum displacement from the equilibrium position. It does not affect the frequency or period of the oscillator, but it does affect the maximum potential and kinetic energy of the system. A larger amplitude results in a greater potential and kinetic energy, while a smaller amplitude results in a lower energy.

5. What are the applications of harmonic oscillators in real-life?

Harmonic oscillators have many practical applications in various fields, including engineering, physics, and biology. Some examples include the use of springs in shock absorbers for vehicles, pendulums in clocks, and the vibration of molecules in chemical reactions. They are also used in musical instruments to produce different notes and frequencies.

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