Simple Harmonic Motion: Limitations of T

In summary, Simple Harmonic Motion (SHM) is a type of periodic motion that occurs in systems with a linear relationship between displacement and restoring force. The period of SHM is the time it takes for one complete cycle of motion, and it has limitations such as only being accurate for small amplitudes of motion and assuming no external forces are acting on the system. These limitations can be overcome by using more advanced mathematical models. Some real-life examples of SHM include pendulums, guitar strings, and masses attached to springs.
  • #1
Hardik Batra
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what is the limitation of T = 2π [itex]\sqrt{\frac{m}{k}}[/itex]
 
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  • #2
Hello Hardik! :smile:

Are you talking about a pendulum?

A pendulum is never exactly shm, but it is very nearly so if we assume θ = sinθ.

Since sinθ = θ - θ3/6 + …

that means the error will be a function of θ2/6 …

to find out what function, just plough through the proof. :wink:




Hardik Batra said:
what is the limitation of T = 2π [itex]\sqrt{\frac{m}{k}}[/itex]
 

1. What is Simple Harmonic Motion (SHM)?

Simple Harmonic Motion is a type of periodic motion in which the restoring force is directly proportional to the displacement from the equilibrium position and is directed towards that position. It occurs in systems where there is a linear relationship between the displacement and the restoring force, such as a mass-spring system.

2. What is the period of Simple Harmonic Motion?

The period of SHM is the time it takes for one complete cycle of motion, from the starting point, through the maximum displacement in one direction, back to the starting point, and then through the maximum displacement in the opposite direction.

3. What are the limitations of the time period, T, in Simple Harmonic Motion?

The time period, T, in SHM has the following limitations:

  • It is only valid for small amplitudes of motion.
  • It assumes no external forces are acting on the system.
  • It assumes the system is in a vacuum with no air resistance.
  • It is only accurate for linear restoring forces, not for nonlinear forces.
  • It is not valid for systems with a large mass compared to the restoring force.

4. How can the limitations of Simple Harmonic Motion be overcome?

The limitations of SHM can be overcome by using more advanced mathematical models, such as the damped harmonic oscillator or the driven harmonic oscillator. These models take into account factors such as friction, air resistance, and nonlinear restoring forces, and can provide more accurate predictions for the motion of a system.

5. What are some real-life examples of Simple Harmonic Motion?

Some examples of SHM in everyday life include the motion of a pendulum, the vibrations of a guitar string, and the motion of a mass attached to a spring. Other examples include the motion of a swing, a bouncing ball, and a mass on a horizontal spring that is stretched and released.

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