Finding ω and T of a Pendulum With No Numbers

In summary, the conversation is about finding the values of ω and T for a pendulum with length L and mass m. The problem provides a picture with symbols for arc length, length, mass, and angle θ. The person tried to solve it using the equation ƩFy=T-mg=0 but is not sure if they made any progress. They prefer having numbers to understand these types of problems and are concerned that the correct answer may be a number. The variables ω and T stand for angular velocity and tension, respectively. The person is unsure if they are overthinking the problem and wonders if their instructor is just testing their understanding. They also discuss the possibility of T not standing for tension and ask if pend
  • #1
NilliNilli
8
0

Homework Statement



All this problem says is to find ω and T of a pendulum with a length L and mass m.
There's a picture of a pendulum labeling the arc length, length, mass, and angle θ with just symbols.

Homework Equations





The Attempt at a Solution



I tried solving algebraically to find T using ƩFy=T-mg=0. I don't know if I made any real progress; I'm not very good at these kinds of problems. I need numbers to really understand these kinds of problems. I'm almost concerned that the correct answer might be a number.
 
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  • #2
Do you know what the variable symbols mean? What is T for instance?
 
  • #3
T is tension. ω is angular velocity. It uses θ for the angle, s for arc length, L for length of the rope/string of the pendulum, and m for mass.
 
  • #4
There's a possibility I'm over-thinking it. My instructor likes to go all-out with some questions, but this might just be him checking out understanding. I'm not sure.
 
  • #5
NilliNilli said:
T is tension. ω is angular velocity. It uses θ for the angle, s for arc length, L for length of the rope/string of the pendulum, and m for mass.
Drawing the free body diagram for the pendulum bob when the pendulum is at angle θ to the vertical, what expression do you get for the tension?
 
  • #6
Are you sure T stands for tension? Are pendulums important in physics because they measure tension?
 

Related to Finding ω and T of a Pendulum With No Numbers

What is the purpose of finding ω and T of a Pendulum With No Numbers?

The purpose of finding ω and T of a pendulum with no numbers is to determine the natural frequency (ω) and period (T) of the pendulum's oscillations. These are important values in understanding the behavior of the pendulum and can be used in various calculations and experiments.

How is ω and T calculated for a Pendulum With No Numbers?

To calculate ω and T of a pendulum with no numbers, we can use the length of the pendulum and the acceleration due to gravity (g) as known values. The formula for ω is √(g/L), where L is the length of the pendulum. T can be calculated using the formula T = 2π/ω.

What factors can affect the accuracy of finding ω and T of a Pendulum With No Numbers?

The accuracy of finding ω and T of a pendulum with no numbers can be affected by various factors such as air resistance, friction, and the precision of the measurement of the pendulum's length. These factors can cause slight variations in the values of ω and T, but they can be minimized by conducting the experiment in a controlled environment and using precise measuring tools.

How is the natural frequency (ω) of a Pendulum With No Numbers related to its length?

The natural frequency (ω) of a pendulum with no numbers is directly proportional to the square root of its length. This means that as the length of the pendulum increases, its natural frequency also increases. This relationship is important in understanding the behavior of pendulums and can be observed in various real-life applications.

Can the values of ω and T change for a Pendulum With No Numbers?

Yes, the values of ω and T can change for a pendulum with no numbers if there are changes in the length of the pendulum or the acceleration due to gravity. However, these changes will be minimal and can be accounted for in the calculations. The values of ω and T will remain relatively constant as long as the length and g are kept constant.

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