Simple pendulum and harmonic motion

In summary, the equation for finding the period of a simple pendulum is T=2pi*(sqrt(L/g)). However, if the pendulum is in an accelerating frame of reference, such as an elevator moving upward at 5.90 m/s2, the equation must be adjusted to account for this acceleration. This can be done by adding the acceleration to the gravitational acceleration in the equation. In this case, the correct answer for the period is 4.58 seconds.
  • #1
Jm4872
12
0

Homework Statement



A simple pendulum is 5.20 m long. What is the period of simple harmonic motion for this pendulum if it is hanging in an elevator that is accelerating upward at 5.90 m/s2?


Homework Equations



T=2pi*(sqrt(L/g))

The Attempt at a Solution



all I did was plug in the value of the length of the pendulum into the equation like so:
T=2pi*(sqrt(5.2/9.8))=4.58s
but this answer is not right? I'm so confused as to what I am supposed to do and why I am given acceleration if I don't even need it.
 
Physics news on Phys.org
  • #2
If you know how to derive this equation you are using, I would go through it and look at where the gravitational acceleration, g, comes in. If the pendulum is feeling a vertical acceleration from the elevator now, in addition to the gravitational acceleration, how would that affect your derivation/equation?
 
  • #3
You're not in a stationary frame of reference. You're in an accelerating frame of reference. Think about it. When you are in an elevator that is accelerating upward (e.g. when it first begins to move) do you feel lighter, heavier, or nothing at all?

It's almost as if a mysterious force has cropped up ;)
 

1. What is a simple pendulum?

A simple pendulum is a weight suspended from a fixed point that can swing back and forth under the influence of gravity. It consists of a string or rod and a mass attached to the end, and is used to demonstrate principles of harmonic motion.

2. What is the period of a simple pendulum?

The period of a simple pendulum is the time it takes for one complete back-and-forth swing, also known as one oscillation. It is dependent on the length of the pendulum and the acceleration due to gravity. The formula for calculating the period is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

3. What is the relationship between the length and period of a simple pendulum?

The length and period of a simple pendulum are inversely proportional, meaning that as the length increases, the period also increases. This relationship is described by the formula T = 2π√(L/g), where T is the period, L is the length, and g is the acceleration due to gravity.

4. What is the difference between simple harmonic motion and regular motion?

Simple harmonic motion is a type of periodic motion where an object moves back and forth in a straight line, while regular motion can occur in any direction. In simple harmonic motion, the acceleration is directly proportional to the displacement from the equilibrium position, and the object's velocity and acceleration are constantly changing. In regular motion, the acceleration can vary in both direction and magnitude.

5. How is simple harmonic motion used in real-life applications?

Simple harmonic motion has many applications in real life, including pendulum clocks, seismometers, and musical instruments. It is also used in engineering to analyze vibrations and oscillations in structures such as bridges and buildings. Understanding the principles of simple harmonic motion is crucial in creating stable and efficient structures and machines.

Similar threads

  • Introductory Physics Homework Help
Replies
14
Views
484
  • Introductory Physics Homework Help
Replies
9
Views
704
  • Introductory Physics Homework Help
Replies
20
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
922
  • Introductory Physics Homework Help
Replies
7
Views
960
  • Introductory Physics Homework Help
Replies
3
Views
703
  • Introductory Physics Homework Help
Replies
1
Views
860
  • Introductory Physics Homework Help
Replies
27
Views
730
  • Introductory Physics Homework Help
2
Replies
51
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
3K
Back
Top