The frequency(/time period) of oscillation for a 2 body spring system

In summary, a 2 body spring system is a type of mechanical system in which two objects are connected by a spring, causing them to oscillate around their equilibrium position. The frequency of oscillation can be calculated using the formula f = 1/2π√(k/m) and is affected by the spring constant, mass of the objects, and amplitude of the oscillations. The time period and frequency of oscillation are inversely related, and the unit for frequency in a 2 body spring system is hertz (Hz).
  • #1
abelthayil
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Homework Statement



Two masses m1 and m2 are connected by a spring of spring constant k rest on a frictionless surface. If the masses are pulled apart and let go, the time period of oscillation is :

I know the answer is T(time period) = 2∏[itex]\sqrt{((m1*m2)/(m1+m2))*1/k}[/itex].
Can some one help me derive this equation. I know the concept is called reduced mass and think it uses the center of mass as the reference frame.
 
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  • #3
Thanks a TON !
 

1. What is a 2 body spring system?

A 2 body spring system is a type of mechanical system in which two objects are connected by a spring. The spring acts as a restoring force, causing the objects to oscillate back and forth around their equilibrium position.

2. How is the frequency of oscillation calculated for a 2 body spring system?

The frequency of oscillation for a 2 body spring system can be calculated using the formula f = 1/2π√(k/m), where f is the frequency, k is the spring constant, and m is the mass of the objects connected by the spring.

3. What factors affect the frequency of oscillation for a 2 body spring system?

The frequency of oscillation for a 2 body spring system is affected by the spring constant, the mass of the objects, and the amplitude of the oscillations. A higher spring constant or lower mass will result in a higher frequency, while a larger amplitude will result in a lower frequency.

4. How does the time period of oscillation relate to the frequency of oscillation?

The time period of oscillation is the amount of time it takes for one full oscillation to occur, while the frequency is the number of oscillations per unit time. These two quantities are inversely related, meaning that as the frequency increases, the time period decreases and vice versa.

5. What is the unit for frequency in a 2 body spring system?

The unit for frequency in a 2 body spring system is hertz (Hz), which is equivalent to 1/second. This unit is commonly used to measure oscillations, vibrations, and waves.

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