# Simple harmonic motion centered at the origin

I'm doing a problem on the simple harmonic motion but I didn't understand it really well.

The problem says: "A point describes a simple harmonic motion centered at the origin, the period is T=0.628s. For t = 0 point's position is x=0.15m etc..."

What it means with "harmonic motion is centered at the origin"? I thought that x=0 when t=0 but this is not right apparently.

• -1. Of course it is not right! The question states that $t=0$ when $x=0.15$. It cannot also be at $x=0$ when $t=0$. It cannot be at two places at the same time. – sammy gerbil Nov 14 '17 at 12:21

The solution is symmetric about $x=0$. Thus, starting from $$x(t)= x_0\cos(\omega t+ \phi)$$ you can derive $\omega$ and the phase $\phi$ from the data of your problem.
A solution not symmetric about the origin would be of the form $$x(t)= A+ x_0\cos(\omega t+ \phi)\, .$$ The harmonic motion would then be "centered" about $A$.
• @Peto this kind of language occurs because one could choose to have $x=0$ at the point where the sho is attached to a wall (if a spring-mass system). Then the equilibrium position would be at some position $\ne 0$. – ZeroTheHero Nov 13 '17 at 16:45
It means that the SHM, in other words the body's oscillations such that its $a \propto x$, are oscillations that are about the origin. It does not necessarily imply that at $t = 0$, $x = 0$. For example, think of a pendulum which starts with from either the left or the right side to the bob's mean position. At $t = 0$, it is starting from a position, $x \neq 0$.
The text passage discusses the concept of simple harmonic motion (SHM) centered at the origin and provides a specific problem where a point undergoes SHM with a given period and initial position. It also includes a comment clarifying a common misconception about the initial conditions of SHM.
no_question

the passage does not contain a direct mathematical question or a request for a calculation. instead, it provides an explanation and a comment to clarify a concept.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Simple harmonic motion centered at the origin

I'm doing a problem on the simple harmonic motion but I didn't understand it really well.

The problem says: "A point describes a simple harmonic motion centered at the origin, the period is T=0.628s. For t = 0 point's position is x=0.15m etc..."

What it means with "harmonic motion is centered at the origin"? I thought that x=0 when t=0 but this is not right apparently.

• -1. Of course it is not right! The question states that $t=0$ when $x=0.15$. It cannot also be at $x=0$ when $t=0$. It cannot be at two places at the same time. – sammy gerbil Nov 14 '17 at 12:21

The solution is symmetric about $x=0$. Thus, starting from $$x(t)= x_0\cos(\omega t+ \phi)$$ you can derive $\omega$ and the phase $\phi$ from the data of your problem.
A solution not symmetric about the origin would be of the form $$x(t)= A+ x_0\cos(\omega t+ \phi)\, .$$ The harmonic motion would then be "centered" about $A$.
• @Peto this kind of language occurs because one could choose to have $x=0$ at the point where the sho is attached to a wall (if a spring-mass system). Then the equilibrium position would be at some position $\ne 0$. – ZeroTheHero Nov 13 '17 at 16:45
It means that the SHM, in other words the body's oscillations such that its $a \propto x$, are oscillations that are about the origin. It does not necessarily imply that at $t = 0$, $x = 0$. For example, think of a pendulum which starts with from either the left or the right side to the bob's mean position. At $t = 0$, it is starting from a position, $x \neq 0$.
user
The text passage discusses the concept of simple harmonic motion (SHM) centered at the origin and provides a specific problem where a point undergoes SHM with a given period and initial position. It also includes a comment clarifying a common misconception about the initial conditions of SHM.

TYPE: NO_QUESTION

The passage does not contain a direct mathematical question or a request for a calculation. Instead, it provides an explanation and a comment to clarify a concept.