# Graphs relating to simple harmonic motion

## Homework Statement  None.

## The Attempt at a Solution

Hi everyone. Apparently 5 is the right answer, although I chose D.

Could anyone please weigh in with their thoughts about why 5 is right and my answer is apparently wrong?

Thanks!

## Answers and Replies

TSny
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Please explain how you got your answer.

Velocity can also be negative...

haruspex
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2020 Award
Velocity can also be negative...
True, but that does not rule out any of the graphs. There is no claim that the graph represents an entire cycle. There is a better reason for choosing 5. What would the graph of velocity actually look like?

Edit: please do not post an answer to that on this thread, at least not until RoboNerd has had a chance to answer it.

Hi everyone, robonerd is back, of course.

I know that at xmin and max, the velocity [with kinetic energy] = 0 instantaneously. Thus, I narrow down to B and D.
However, I know that with a variable spring force giving a variable acceleration, I will not have the velocity changing in a linear manner [constant acceleration with constant slope], so I rule out B. D is thus a potential answer. Why is D wrong?

haruspex
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2020 Award
Hi everyone, robonerd is back, of course.

I know that at xmin and max, the velocity [with kinetic energy] = 0 instantaneously. Thus, I narrow down to B and D.
However, I know that with a variable spring force giving a variable acceleration, I will not have the velocity changing in a linear manner [constant acceleration with constant slope], so I rule out B. D is thus a potential answer. Why is D wrong?
Can you write an equation relating velocity and x?

Yes. Using conservation of energy I have:

( 1 / 2 ) * k * A^2 = a constant value = (1 / 2) * m * v^2 + ( 1/ 2) * k * x^2

haruspex
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2020 Award
Yes. Using conservation of energy I have:

( 1 / 2 ) * k * A^2 = a constant value = (1 / 2) * m * v^2 + ( 1/ 2) * k * x^2
Good. Can you recognise that form as a common shape? (Think of v as the y coordinate.)