Question

w will the time period of a simple harmonic pendulum change if its length is double?​

Answer 1

Explanation:

Time period is directly proportional to the length. So if length is doubled the time period is doubled.

Answer 2

Answer:

4

What will happen to the time period of a simple pendulum if its length is doubled?

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Gage Koskovich

Updated February 16, 2018

What does the effect of the time period of a simple pendulum if its length is doubled?

Good question! To figure this out let’s assume that we have two pendulums that we want to study. The first will have a standard length, the second will have double the length. Now, we can model the period of each pendulum with the following equation:

T=2πLg−−√

Using this equation (and some algebra) we’re going to model the two cases and compare each respective period. To do so, we need to find a way to set the equations equal to each other. This can be done by solving for gravity (g) as follows:

T=2πLg−−√

T2π=Lg−−√

(T2π)2=Lg

g=L(2πT)2

Now that we’ve solved for the first scenario, we can use the same process to solve for the second scenario:

T′=2π2Lg−−−√

T′2π=2Lg−−−√

(T′2π)2=2Lg

g=2L(2πT′)2

Here’s where the comparison begins. Since we want to understand the second case in terms of the first, our goal will be to solve the equation for T’. Let’s begin by setting the two equations equal to each other because as we know: “Things that are equal to the same thing must be equal to each other.” This is known as transitivity and it’s a very useful tool when approaching questions like this one.

L(2πT)2=2L(2πT′)2

(2πT)2=2(2πT′)2

(2πT)=2–√(2πT′)

1T=2√T′

T′=2–√T

There it is! But what does it mean? Well, it means that the period of the second pendulum is going to be just a little bit longer than the first.

Using this same method of comparison we can infer quite a lot from the equations we find throughout our journey in physics. This is an invaluable tool for when studying new concepts as it allows you to conceptualize the problems you’ll be facing. Anyways, I’ll stop rambling…

Hope this helps! : )