# How Does Amplitude Affect Total Distance Traveled in SHM?

• Shiina-kun
In summary, the conversation is about a student seeking help with a physics homework problem involving vibrations and waves. They are struggling to determine which formula to use to solve the problem and are questioning if they have enough information. The formulas mentioned include those dealing with amplitude. The expert provides the formula for calculating the radius of a circle given its area, which could potentially help solve the problem.
Shiina-kun

I'm having trouble with my physics homework. I can't seem to figure out which formula to use to solve a particular problem.

"If a particle undergoes SHM with amplitude 0.25m, what is the total distance it travels in one period?"

The formulas I have that deal with amplitude are:
$$V$$= $$\pm$$$$V{o}$$$$\sqrt{1 - x^{2}/A^{2}}$$

$$V$$=$$A\sqrt{k/m}$$

x=$$Acos2$$* $$\pi$$(frequency)t​
I don't know which formula to use because it seems like I don't have enough information for any of them. Could someone please tell me which formula to use and why?

A=4(pi)r^2
so r=sqrt(A/4pi)

so:
r=sqrt(0.25m/12.57)=.020m

Hi there,

Based on the information given, it seems like you are dealing with simple harmonic motion (SHM), where the particle moves back and forth in a periodic manner. In this case, the total distance traveled in one period is equal to the amplitude of the motion, which in this case is 0.25m. This is because in SHM, the particle moves from its equilibrium position (where x=0) to its maximum displacement (amplitude) and back to the equilibrium position in one period.

Therefore, the formula you need to use is x=Acos(2πft), where x is the displacement, A is the amplitude, f is the frequency, and t is time. In this case, you are given the amplitude (0.25m) and you can assume a value for the frequency (e.g. 1Hz or 2π rad/s) to solve for the total distance traveled.

I hope this helps! If you are still having trouble, I suggest discussing it with your teacher or seeking help from a tutor or classmate. Good luck with your homework!

## What are vibrations and waves?

Vibrations and waves are disturbances that travel through a medium, such as air or water, transferring energy from one place to another.

## What causes vibrations and waves?

Vibrations and waves can be caused by various sources, such as mechanical motion, electromagnetic radiation, or sound waves.

## What is the difference between vibrations and waves?

Vibrations are oscillations that occur in one place, while waves are the transfer of energy through a medium from one place to another.

## How are vibrations and waves measured?

Vibrations and waves can be measured using various units, such as frequency, amplitude, and wavelength, depending on the type of wave being studied.

## What are some real-world applications of vibrations and waves?

Vibrations and waves have numerous applications in everyday life, such as in music, communication technology, medical imaging, and earthquake detection.

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