How Is the Period of a Pendulum Affected by Its Length?

In summary: Anyway, I think I understand now. I was able to solve the equation and get an answer for the initial length, which was approximately 3.09047 meters. Plugging this back into the equation T = 2π√(l/g), I got an answer of approximately 3.525678 seconds for the initial period of oscillation. In summary, to increase the period of oscillation of a pendulum in 1 second, you need to increase the length by 2 meters. Using the equation T = 2π√(l/g), you can solve for the initial period of oscillation, which is approximately 3.525678 seconds.
  • #1
Ethxn
5
0
Member advised to use the homework template for posts in the homework sections of PF.
To increase the period of oscillation of a pendulum in 1 second, it is needed to increase the length of it in 2 meters. Calculate, in seconds, of the initial period of oscillation of the pendulum.

I found this question online a few minutes ago. I have not learned this in physics class yet so bare with me :)
Because it is asking for the period of the oscillation I figured I would need the equation: T = 2π√(l/g)

To set up the equation, I wrote it like this

2π√(l/g) + 1 = 2π√(l+2/g)

as the period of the oscillation increased by one when the length increased by 2 meters. When I solve this equation though, everything except cancels itself out, so I can't find the initial length to plug back into the equation to find the initial period... Again, I am 1 month in of my first year of physics so don't crucify me for my mistakes please (lol), and the wording on this question is quite confusing too, so I may have it all wrong but hopefully you can see where I'm going with this ;)

Thanks in advance!
 
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  • #2
I think you set it up correctly. Try squaring both sides, cancelling the terms that cancel, and then grouping terms and squaring once more. If you are careful with the algebra, you should get an answer for "l". (You do need a parentheses around your (l+2).)
 
  • #3
I only put the parentheses around the l/g to show that it was included in the square root. Anyway, you can take a look at my work:
0cfc21fbc2e419d27f0295d07110d6f3.jpg
Unless I messed it up, the lengths do in fact cancel each other out. :/
 
  • #4
Ethxn said:
I only put the parentheses around the l/g to show that it was included in the square root. Anyway, you can take a look at my work:
0cfc21fbc2e419d27f0295d07110d6f3.jpg
Unless I messed it up, the lengths do in fact cancel each other out. :/
How about the 2ab term when you square the left side? ## (a+b)^2=a^2+2ab+b^2 ##.
 
  • #5
ohhhhh... I completely forgot. So now when I solve the equation, I get about 3.09047 for the initial length. When I put this back into the equation T = 2π√(l/g) I got about 3.525678 seconds. I am not sure if it is correct yet but thanks a lot for the help!
 
  • #6
Ethxn said:
ohhhhh... I completely forgot. So now when I solve the equation, I get about 3.09047 for the initial length. When I put this back into the equation T = 2π√(l/g) I got about 3.525678 seconds. I am not sure if it is correct yet but thanks a lot for the help!
I didn't compute an exact answer either, but that's approximately what I got. Good work !
 
  • #7
"in 1 second" = "by 1 second" or "to 1 second"?
 
  • #8
CWatters said:
"in 1 second" = "by 1 second" or "to 1 second"?

The person who asked this problem meant "by." I just copied the problem down verbatim in case that wasn't the case.
 

Related to How Is the Period of a Pendulum Affected by Its Length?

1. What is an oscillation?

An oscillation is a repeated back-and-forth or up-and-down motion of an object or system. It can be seen in many different contexts, such as a swinging pendulum, a vibrating guitar string, or the movement of air molecules as sound waves.

2. What causes oscillations?

Oscillations are caused by a restoring force, which is a force that acts to return an object or system to its equilibrium position. This force can be gravity, tension, or elasticity, depending on the specific situation.

3. How are oscillations measured?

The amplitude, frequency, and period are the three main measurements of an oscillation. The amplitude is the maximum displacement from the equilibrium position, the frequency is the number of oscillations per unit of time, and the period is the time it takes for one complete oscillation.

4. What is resonance and how does it relate to oscillations?

Resonance is a phenomenon that occurs when an oscillating system is driven by a periodic force that has the same frequency as the natural frequency of the system. This causes the amplitude of the oscillations to increase significantly, which can have both beneficial and destructive effects depending on the situation.

5. What are some practical applications of oscillations?

Oscillations have a wide range of practical applications in various fields of science and engineering. Some examples include the use of pendulums in clocks, the measurement of seismic waves in earthquakes, and the production of sound in musical instruments. They are also used in technologies such as lasers, radios, and MRI machines.

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