Simple Harmonic otion (1 Viewer)

[goobi]

Simple Harmonic Motion

This is a question from Math in Focus.

The period of a particle moving in *EDIT* SHM is 6s and its amplitude is 8cm. Calculate its velocity and acceleration (correct to 1 decimal place) when the displacement is 5cm from the centre of the motion.

Okay so these are what I've done so far:






(cor. to 1 d.p.)

However, the problem is I don't understand why the textbook takes the negative sign (i.e. -6.5 cm/s) instead of the positive sign. I thought the velocity was supposed to be in the same direction as the displacement (i.e +5cm as given)? Correct me if I am wrong.

Any help would be greatly appreciated

 

[Carrotsticks]

Just because the displacement is positive, doesn't necessarily mean that the velocity is negative.

Suppose I'm walking on a number line and I pass the point X=5.

To go through this point, I could either be going to the left or the right.

If I'm walking towards positive infinity (ie: my path goes x=5,6,7...), then my velocity is considered *EDIT* positive (accidentally type 'negative')

However if I'm walking towards negative infinity (ie: my path goes x=5,4,3...), then my velocity is considered negative since I am walking in the negative direction.

In my opinion, the solutions are incorrect. I would say that the velocity is |6.5m/s| because it just says 5cm from the centre of motion.

It didn't say whether the particle was returning from the endpoint (negative velocity) or going towards the endpoint (positive velocity).

 

[Carrotsticks]

Also, inb4"goobypls"

 

[goobi]

Just because the displacement is positive, doesn't necessarily mean that the velocity is negative.

In my opinion, the solutions are incorrect. I would say that the velocity is |6.5m/s| because it just says 5cm from the centre of motion.

It didn't say whether the particle was returning from the endpoint (negative velocity) or going towards the endpoint (positive velocity).

Thanks mate! But I don't understand why you take the absolute value of 6.5m/s as we are finding the velocity but not the speed?
Edit: Or does the absolute sign indicate that the velocity can either be positive or negative?

 

[Mature Lamb]

gooby pls

 

[iSplicer]

gooby pls =]

 

[Carrotsticks]

Thanks mate! But I don't understand why you take the absolute value of 6.5m/s as we are finding the velocity but not the speed?
Edit: Or does the absolute sign indicate that the velocity can either be positive or negative?

It's because based on the information we are given, we cannot conclude from which direction the particle is coming, so we can't conclude whether it's positive or negative.

Hence I would put the absolute value.

gooby pls

gooby pls =]

Haha you guys.