What is time average of tension?

For small angles as you have here, the force balance is F = ma = m d^2 theta/dt^2. The forces acting on the mass are the tension in the string T and the weight mg. You assume that the tension in the string and the angle theta are both functions of time. You then solve the differential equation for theta(t). In summary, the homework question involves a simple pendulum undergoing small oscillations and asks whether the time average of the tension in the string is larger or smaller than mg, and by how much. The approach to solving this problem is to use the force balance equation, F = ma = m d^2 theta/dt^2, and solve for theta as a function of time
  • #1
lemon__meringue
1
0
Summary: My homework question asks: Consider a simple pendulum, undergoing small oscillations. Is the time average of the tension in the string of the pendulum larger or smaller than mg? By how much?

My homework question asks: Consider a simple pendulum, undergoing small oscillations. Is the time average of the tension in the string of the pendulum larger or smaller than mg? By how much?

I tried to use T= mgcosθ - mv^2/L to find the angle in terms of time and then use the average of a function things which I learned in calc. But I have no idea how to go about finding θ (t) . Is this right thought the process? or is there a better way? Please help me :'(

Thanks for any help in advance
 
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  • #2
Welcome to PF. I moved it to a homework help forum. Next time you have a homework problem, post it in the homework forum and fill out the template the forum will provide.

Here's a hint. How much is the tension if the small oscillations are zero in size? In other words, standing still.
 
  • #3
You find theta as a function of time by solving the force balance in the tangential direction.
 

FAQ: What is time average of tension?

1. What is the definition of time average of tension?

Time average of tension is a measurement that calculates the average amount of tension or force exerted over a period of time. It is used to describe the overall stress or strain on an object or system.

2. How is time average of tension different from instantaneous tension?

Instantaneous tension measures the amount of force or tension at a specific moment in time, while time average of tension takes into account the average force over a period of time. It provides a more comprehensive understanding of the overall tension on a system.

3. What factors affect the time average of tension?

The time average of tension can be affected by various factors such as the magnitude and frequency of the applied force, the material properties of the object or system, and any external factors that may influence the tension.

4. How is time average of tension calculated?

The time average of tension is calculated by taking the integral of the tension function over a specific time period and dividing it by the length of the time interval. This can be represented by the formula: Tavg = (1/T) * ∫F(t)dt, where T is the time interval and F(t) is the tension function.

5. Why is time average of tension important in scientific research?

Time average of tension is important in scientific research as it provides a more accurate and comprehensive understanding of the stress and strain on an object or system. It allows scientists to analyze and predict the behavior of materials and structures, and make informed decisions about their design and use.

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