Simple Harmonic Motion and frequency of a spring

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  • #1
kidia
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I have one question here,I fail to understood what is Q of the system,is anybody has an ideal on this?

An object of mass 2 kg hangs from spring of negligible mass. The spring is extended by 2.5 cm when the object is attached. The top end of the spring is oscillated up and down in SHM with amplitude of 1 mm. The Q of the system is 15.

What is angular frequency for this system?
 
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  • #2
kidia said:
I have one question here,I fail to understood what is Q of the system,is anybody has an ideal on this?

"Q" is just a symbol until it is given a definition. What does your book say about it? What do your class notes say about it?

An object of mass 2 kg hangs from spring of negligible mass. The spring is extended by 2.5 cm when the object is attached. The top end of the spring is oscillated up and down in SHM with amplitude of 1 mm. The Q of the system is 15.

The system will certainly not execute SHM. It is driven by gravity.

What is angular frequency for this system?

What have you tried so far?
 
  • #3
Sounds like Q is the frequency.
 
  • #4
kidia said:
I have one question here,I fail to understood what is Q of the system,is anybody has an ideal on this?

An object of mass 2 kg hangs from spring of negligible mass. The spring is extended by 2.5 cm when the object is attached. The top end of the spring is oscillated up and down in SHM with amplitude of 1 mm. The Q of the system is 15.

What is angular frequency for this system?

Q is the quality factor. it is an indirect measure of the damping. A large Q means that the damping is small, the oscillation takes a while to die off (assuming no external force of course).

If I recall, [itex] Q = { \omega_d \over (b/m) }= {m \omega_d \over b} [/itex]

where [itex] \omega_d \approx \omega_0[/itex].
From the fact that spring extends 2.5 cm with a mass of 2 kg you can find the spring constant. So you know omega_0. Knowing Q then gives you a way to find the damping constant. I am not sure about the rest of the steps, though...

Pat
 

Related to Simple Harmonic Motion and frequency of a spring

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object moves back and forth along a straight line, with its acceleration proportional to its displacement from a fixed point. This type of motion is seen in systems such as a mass-spring system or a pendulum.

2. How is the frequency of a spring related to its mass and spring constant?

The frequency of a spring is inversely proportional to the square root of its mass and directly proportional to the square root of its spring constant. This can be expressed as the formula f = 1/(2π)*√(k/m), where f is the frequency, k is the spring constant, and m is the mass.

3. What is the significance of resonance in simple harmonic motion?

Resonance occurs when the frequency of an applied force matches the natural frequency of a system, causing the amplitude of the motion to increase significantly. In the case of simple harmonic motion, resonance can occur in systems such as a mass-spring system or a pendulum, and can be used to amplify the motion of the system.

4. How does damping affect the motion of a spring?

Damping is the gradual loss of energy in a system, and it can affect the amplitude and frequency of simple harmonic motion in a spring. In an ideal system, where there is no damping, the amplitude and frequency of the motion remain constant. However, in a damped system, the amplitude decreases and the frequency may change as energy is lost due to friction or other factors.

5. How is the period of a spring related to its frequency?

The period of a spring is the time it takes for one complete cycle of motion, while the frequency is the number of cycles per unit of time. The two are inversely related, meaning that as the frequency increases, the period decreases. This can be expressed as the formula T = 1/f, where T is the period and f is the frequency.

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