To find the length of a pendulum in Simple Harmonic motion

In summary: E2%80%93+what+does+the+%E2%80%9Cin+step%E2%80%9D+term+mean+and+what+does+it+mean+for+two+pendulums&p=5609295#post5609295In summary, the "in step" term means that the two pendulums are in the same position and have the same velocity. This is important for understanding the problem statement, since it is referencing whether or not the shorter one was in step at the first time the two met.
  • #1
Yehia11
14
0
If we have 2 simple pendulums, (one longer than the other) oscillating in SHM in step. The next time they are in step is after 20 seconds has elapsed, during which the time the longer pendulum has completed exactly 10 oscillations. Find the string lengths

I found that the length of the long one is 1 metre through the equation:

Periodic Time (which is 2) = 2pi X root(l/g)

but how do we find the length of the longer one??

thankyou in advance. help very appreciated!
 
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  • #2
Is this homework? If so it should be in the homework section.

Torquil
 
  • #3
torquil said:
Is this homework? If so it should be in the homework section.

Torquil

It is not homework, so no, it should not be in the homework section.
 
Last edited:
  • #4
Sorry, but I think it is good to ask whenever there is a problem that looks "homework-like". Don't take it personally.

Anyway, the shorter (and faster) pendulum must have completed exactly 11 periods when they are in step for the first time, since the longer one has completed exactly 10.

Thus the pendulum periods satisfy T_long * 10 = T_short * 11.

This gives you T_short which is slightly smaller than T_long, and you can use your formula to calculate its length.

Torquil
 
  • #5
Yehia11 said:
but how do we find the length of the longer one??

Just to clarify, you meant to say "shorter one" here, right? Because you have already found the length of the longer one to be approximately 1m. Anyway, if my calculation mixes this up, just modify my numbers a bit (the 10 and 11 in my formula) to fit with the exact problem. The idea is the same.

Torquil
 
  • #6
No problem, sorry if i sounded antagonistic, no harm in asking.

Anyway, firstly YES your right I did mean the SHORTER one, sorry my bad. We know the length of the longer one, it is the shorter one we are trying to find. :)

And secondly why must the shorter one have completed exactly 11 cycles? we know that the long one (and slower one) completed 10, but i feel we have too little info about the short one? or am i wrong? thank you very much for your input, i appreciate it.
 
  • #7
First, the shorter one must have completed an exact whole number of periods, since the two pendulums meet when the longer one has completed an exact whole number of periods.

In addition, if the shorter one has completed more than one extra period (ie. a total of 12 of more), then they would have been in step much earlier, since it would have had to overtake the longer one at least once before t=20s. So then it would not be true that it was the first time they were in step. Therefore the shorter one must have completed exactly one more period than the longer one.

E.g. if the shorter one had completed 12 in that time, they would have been in step after 10s also, which is not true according to the problem statement. If the shorter one had completed 13, they would have been in step after exactly 20/3 seconds, and so on.

I'm assuming that "in step" means being at the same position with a velocity in the same direction.

Torquil
 

1. What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion in which a system oscillates back and forth around an equilibrium point, with a restoring force that is proportional to the displacement from the equilibrium point. This means that the further the system is displaced, the stronger the restoring force will be, causing the system to oscillate with a constant frequency.

2. How is the length of a pendulum related to Simple Harmonic Motion?

A pendulum is a classic example of a system exhibiting Simple Harmonic Motion. The length of the pendulum is directly related to the period (time for one complete oscillation) of the pendulum's motion. The longer the length of the pendulum, the longer the period will be.

3. What factors affect the length of a pendulum in Simple Harmonic Motion?

The length of a pendulum in Simple Harmonic Motion is affected by three main factors: gravity, the mass of the pendulum, and the angle of displacement. Gravity is the force that provides the restoring force for the pendulum's oscillation. The mass of the pendulum affects the inertia of the system, which in turn affects the period of oscillation. And the angle of displacement also affects the period, as it changes the distance the pendulum needs to travel in each oscillation.

4. How can the length of a pendulum in Simple Harmonic Motion be calculated?

The length of a pendulum in Simple Harmonic Motion can be calculated using the equation: L = (g * T^2)/(4 * pi^2), where L is the length of the pendulum, g is the gravitational acceleration, and T is the period of oscillation. This equation assumes that the angle of displacement is small (less than 15 degrees) and that the mass of the pendulum is concentrated at its end.

5. What is the significance of finding the length of a pendulum in Simple Harmonic Motion?

Finding the length of a pendulum in Simple Harmonic Motion allows us to better understand and predict the behavior of pendulums and other systems that exhibit SHM. It also has practical applications, such as in the design of accurate clocks and other timekeeping devices. Additionally, studying the length of a pendulum in SHM can help us further understand the laws of motion and the concept of periodic motion in general.

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