Solve Period of a Pendulum Equation | Physics Forum

In summary, the conversation is about a user seeking help in proving an equation involving physics concepts. They have received some advice but are still struggling with removing a variable from the equation. The equation is an approximation and is most accurate when the sine function is equal to x in radians. The user is specifically trying to prove that the angular velocity is equal to the square root of g/L.
  • #1
Hootenanny
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I have already posted in the physics forum but its gone a bit quiet. I've managed to derrive an equation up to this point. I have [tex]\frac{g}{L}\theta = \omega^2 \theta_{max} \sin (\omega t - \alpha) [/tex] and I need to prove that [tex] \omega = \sqrt{\frac{g}{L}} [/tex]. I'm stuped at this one. Thank's in advance for your help.
 
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  • #2
well, you need to know that it's only an approximation. It is most accurate when sinx=x (in radians of course).
 
  • #3
That doesn't help me much all that gives then is [tex]\frac{g}{L}\theta = \omega^2 \theta_{max}(\omega t - \alpha) [/tex]
 
  • #4
Now I have [tex]\theta = \theta_{max} \sin(\sqrt{\frac{g}{L}} t - \alpha ) [/tex] How Can I remove the [itex]\alpha [/itex] ?
 

1. What is the equation for calculating the period of a pendulum?

The equation for calculating the period of a pendulum is T = 2π√(L/g), where T is the period (in seconds), L is the length of the pendulum (in meters), and g is the acceleration due to gravity (9.8 m/s²).

2. How is the length of a pendulum related to its period?

The length of a pendulum is directly proportional to its period. This means that as the length of the pendulum increases, the period also increases. This relationship is expressed in the equation T = 2π√(L/g).

3. Can the period of a pendulum be affected by other factors?

Yes, the period of a pendulum can be affected by factors such as the mass of the pendulum, the amplitude (angle) of the swing, and air resistance. These factors can alter the acceleration due to gravity and therefore affect the period of the pendulum.

4. How does the acceleration due to gravity vary on different planets?

The acceleration due to gravity varies on different planets based on their mass and radius. For example, on Earth, the acceleration due to gravity is 9.8 m/s², but on the moon, it is only 1.6 m/s². This means that the period of a pendulum would be longer on the moon compared to Earth.

5. What is the significance of the period of a pendulum?

The period of a pendulum is significant because it is a constant value that can be used to accurately measure time. This property has been utilized in pendulum clocks, which were widely used before the invention of more accurate timekeeping devices. The period of a pendulum is also important in studying oscillatory motion and understanding concepts of energy and damping in physics.

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