# What are the correct conditions for Simple Harmonic Motion?

• Bolter
In Summary, the multiple choice questions ask about the conditions of SHM, which is a type of periodic motion or oscillation motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. Option C is the best answer, as it matches in with the definition given in my head.
Bolter
Homework Statement
See below
Relevant Equations
None
Ok so here are a few multiple choice questions that I have been given to me and these are what my selected options turned out to be

Do they seem right?

I am rather confused on the wording of the first question?

Is it asking to state the conditions of SHM for it be in SHM?
I know that from the definition in my head SHM is a type of periodic motion or oscillation motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement

I know it must be option C as that matches in with the above definition I had given. Cannot be option B as it simply just says motion on a pendulum or spring but does not describe any features of SHM. But option A is describing Hooke's law and says nothing about the displacement or how acceleration is directly proportional to its displacement from equilibrium position?

Any help would be appreciated! Thanks

Q1. I'd agree with you that( a) is almost the same as (c), but (c) is a bit more general, so better.

Q2. Again, I'd vote (c) as best answer. I don't like (b) because Θ is undefined and I think angular velocity needs to be about some point/axis , but (b) might be liked by people here because it is mathematical rather than words. I'll wait to see what they come up with.

Q3. correct, (b).

Q4. This one I find most difficult. My first reaction was to prefer (b) as the general definition of period, rather than (c) which seems to me to be a mathematical consequence of the definition of SHM.
On further reflection (& re-reading the question) (c), being a consequence of SHM is actually an advantage, when the question asks for a definition specifically of period for SHM. So I'll go for (c) despite my loathing of math's taking ownership of physics!

Bolter
Merlin3189 said:
Q1. I'd agree with you that( a) is almost the same as (c), but (c) is a bit more general, so better.

Q2. Again, I'd vote (c) as best answer. I don't like (b) because Θ is undefined and I think angular velocity needs to be about some point/axis , but (b) might be liked by people here because it is mathematical rather than words. I'll wait to see what they come up with.

Q3. correct, (b).

Q4. This one I find most difficult. My first reaction was to prefer (b) as the general definition of period, rather than (c) which seems to me to be a mathematical consequence of the definition of SHM.
On further reflection (& re-reading the question) (c), being a consequence of SHM is actually an advantage, when the question asks for a definition specifically of period for SHM. So I'll go for (c) despite my loathing of math's taking ownership of physics!

Ok thanks this has definitely cleared up a bit of misunderstanding that I had :) This was helpful

## 1. What is SHM (Simple Harmonic Motion)?

SHM is a type of periodic motion in which the restoring force is directly proportional to the displacement from equilibrium and acts in the opposite direction of the displacement. In simpler terms, it is a motion where the object oscillates back and forth around a central point, with a constant frequency and amplitude.

## 2. What are the conditions for SHM?

The conditions for SHM are: 1) The restoring force must be directly proportional to the displacement from equilibrium, 2) The restoring force must act in the opposite direction of the displacement, and 3) The motion must be periodic, meaning the object returns to its original position after a certain amount of time.

## 3. What is the equation for SHM?

The equation for SHM is x = A cos(ωt + φ), where x is the displacement from equilibrium, A is the amplitude, ω is the angular frequency, and φ is the phase angle.

## 4. What is the relationship between SHM and circular motion?

SHM and circular motion are closely related. In fact, SHM can be thought of as a projection of circular motion onto a straight line. This means that the equations and principles used to describe circular motion can also be applied to SHM.

## 5. What are some real-life examples of SHM?

Some common examples of SHM include a pendulum, a mass on a spring, and a swinging door. Other examples include the motion of a vibrating guitar string, a child on a swing, and the motion of a tuning fork.

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