# Simple Harmonic Motion - Conflicting equations

• jumbogala
In summary, the equation for the displacement of a sine wave in simple harmonic motion is x(t) = Acos(ωt + ɸ0). However, for a sine wave traveling to the left in a medium with frequency 200 Hz, speed 400 m/s, amplitude 0.010 m, and initial phase 90 degrees, the equation y(x,t) = Asin(ωt - kx + ɸ0) should be used with a small modification. The first equation is the general equation for SHM, while the second equation is specifically for a sine wave propagating in a medium towards the positive x direction. The extra term -kx in the second equation accounts for the direction of propagation.
jumbogala

## Homework Statement

What is the equation for the displacement of a sin wave (eg something in SHM)?

My book says x(t) = Acos(ωt + ɸ0)

My prof's notes say y(x,t) = Asin(ωt - kx + ɸ0)

## The Attempt at a Solution

I'm not confused about why one is sin and the other is cos. I'm confused why one has the extra term -kx. When do you use which?

I have a question that asks me to write the displacement for a sine wave traveling to the left with frequency 200 Hz, speed 400 m/s, amplitude 0.010 m, and initial phase 90 degrees. So I'm not sure which of the above to use.

First one is the general equation of SHM.
The second one the equation of the sine wave propagating in a medium towards the positive x direction.
You have to use the second equation to find the displacement with a small modification.

## 1. What is Simple Harmonic Motion?

Simple Harmonic Motion is a type of periodic motion in which an object oscillates back and forth around an equilibrium position, with a restoring force proportional to the displacement from the equilibrium point.

## 2. What are the conflicting equations for Simple Harmonic Motion?

The two conflicting equations for Simple Harmonic Motion are x = A sin(ωt + φ) and x = A cos(ωt + φ), where x is the displacement, A is the amplitude, ω is the angular frequency, and φ is the phase angle.

## 3. How do these equations differ from each other?

The main difference between the two equations is the starting point of the oscillation. In the sine equation, the object starts at its maximum displacement, while in the cosine equation, the object starts at its equilibrium position. This leads to a phase difference of π/2 between the two equations.

## 4. Why are these equations considered conflicting?

These equations are considered conflicting because they represent two different ways of mathematically describing the same motion. This can lead to confusion and inconsistency in solving problems related to Simple Harmonic Motion.

## 5. How can one resolve the conflict between these equations?

The conflict between these equations can be resolved by choosing one equation and consistently using it throughout a problem. It is also important to understand the differences between the two equations and how they affect the values of the variables. Additionally, one can use trigonometric identities to convert between the sine and cosine equations if needed.

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