# Is this Simple Harmonic Motion?

• solarmidnightrose
In summary, the conversation discussed the concept of Simple Harmonic Motion (SHM) and its application in real life. It was clarified that while many examples in real life may exhibit Harmonic Motion, they may not necessarily follow SHM. The conversation also addressed the possibility of doing calculations related to SHM for such examples. It was concluded that while SHM is a working approximation in many cases, there are always factors that may deviate from the ideal conditions.
solarmidnightrose
I've been going to the theme park almost every year-and this year in my Physics class we are learning mechanics, more specifically Simple Harmonic Motion.
My teacher told us that for an object to have 'Simple Harmonic Motion' it must have oscillatory motion (like a pendulum going back and forth).

Here is the link to a short video of the ride at the theme park I go to: (just skip the video to about the 1/2 way mark).

I was wondering if this follows SHM?

I'm a bit confused because the swinging part of the ride gets successively higher as the ride proceeds.

And I'm wondering if the rotating part of the ride affects the SHM? because in a 'normal pendulum demo', the bob doesn't rotate/spin as it oscillates.

No, this is not simple harmonic motion and there are many reasons for it.
1. As you have noticed, energy is clearly being put into the motion as the amplitude increases.
2. A pendulum is generally not undergoing SHM. If your teacher claims this he is wrong. For SHM it is not sufficient for the motion to be periodic and the motion of a pendulum is only well approximated by SHM if the amplitude is very small. This is clearly not the case here.
3. Regarding the rotation, it is a bit unclear which part of the ride you are asking about the SHM for. It is clearly not the case that the people on the ride are in SHM.

solarmidnightrose
solarmidnightrose said:
we are learning mechanics, more specifically Simple Harmonic Motion.
Most examples in real life may be Harmonic Motion - just not Simple.
SHM can be described by a basic sine wave in time. Even the familiar pendulum is not exactly SHM. The nearest we get to mechanical SHM is a mass bouncing on a good, uniform spring. That relies of good old Hooke's Law which tells us that a spring follows a linear relationship between force and extension.

Orodruin said:
No, this is not simple harmonic motion and there are many reasons for it.
1. As you have noticed, energy is clearly being put into the motion as the amplitude increases.
2. A pendulum is generally not undergoing SHM. If your teacher claims this he is wrong. For SHM it is not sufficient for the motion to be periodic and the motion of a pendulum is only well approximated by SHM if the amplitude is very small. This is clearly not the case here.
3. Regarding the rotation, it is a bit unclear which part of the ride you are asking about the SHM for. It is clearly not the case that the people on the ride are in SHM.
So, as this is not SHM, is it still possible to do calculations related to SHM?

things such as:
• amplitude
• frequency
• period
• angular velocity/acceleration

sophiecentaur said:
Most examples in real life may be Harmonic Motion - just not Simple.
SHM can be described by a basic sine wave in time. Even the familiar pendulum is not exactly SHM. The nearest we get to mechanical SHM is a mass bouncing on a good, uniform spring. That relies of good old Hooke's Law which tells us that a spring follows a linear relationship between force and extension.
Thank you for making this clear :)

solarmidnightrose said:
So, as this is not SHM, is it still possible to do calculations related to SHM?
I think this is a matter of degree. We describe a Radio Signal in terms of its centre / main frequency which is treating it as a sinusoidal variation of volts. But then we acknowledge that it carries information which implies that it takes up a significant bandwidth. It is not a sine wave BUT that approximation works fine for antenna and amplifier design.
Basically we are in the real world and SHM is a working approximation in many cases. But there is always a caveat.

## 1. What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion in which an object oscillates back and forth around an equilibrium point with a constant amplitude and a constant period. It is commonly seen in systems with a restoring force that is proportional to the displacement from the equilibrium point, such as a mass attached to a spring.

## 2. How do you know if something is exhibiting Simple Harmonic Motion?

To determine if an object is exhibiting Simple Harmonic Motion, we need to look for three key characteristics: a constant amplitude, a constant period, and a restoring force that is proportional to the displacement from the equilibrium point. If all three of these conditions are met, then the motion can be considered simple harmonic.

## 3. What are the equations for Simple Harmonic Motion?

The equations for Simple Harmonic Motion are: x = A cos(ωt), v = -ωA sin(ωt), and a = -ω^2A cos(ωt), where x is the displacement from the equilibrium point, A is the amplitude, ω is the angular frequency, t is time, v is the velocity, and a is the acceleration.

## 4. Can real-world systems exhibit Simple Harmonic Motion?

Yes, real-world systems can exhibit Simple Harmonic Motion. Some examples include a mass attached to a spring, a pendulum, and a vibrating guitar string. However, in most cases, these systems experience some amount of damping, which causes the amplitude to decrease over time.

## 5. What is the importance of Simple Harmonic Motion in science and engineering?

Simple Harmonic Motion is important in science and engineering because it is a fundamental type of motion that can be used to model and understand more complex systems. It also has many practical applications, such as in the design of suspension systems, musical instruments, and clocks.

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