You are Here: Home >< Physics

# Simple Harmonic Motion Question

Announcements Posted on
Would YOU be put off a uni with a high crime rate? First 50 to have their say get a £5 Amazon voucher! 27-10-2016
1. Hi. My Physics teacher never explains anything, and there's something I'm very confused about. I need to know before school starts again, so I'm asking here.
***I'm using w for the small letter omega.***

At a random position in SHM, displacement is given as
x=Acos(wt), where A is the amplitude.

To find the equation for velocity at that point, you just derive it. The derivation of cos(x) is -sin(x). All is fine so far.

What I'm confused about is why the equation is x= -wAsin(wt), and not just
x= -Asin(wt). Where does the extra omega come from??

I've noticed that when you derive it again, you get w^2, so clearly it is multiplied by w each time, but I can't work out why.

I've asked a few people and nobody could explain it to me. No one is my class seems to have any idea either.

Any and all help is greatly appreciated. Thanks!
2. (Original post by JustJusty)
Hi. My Physics teacher never explains anything, and there's something I'm very confused about. I need to know before school starts again, so I'm asking here.
***I'm using w for the small letter omega.***

At a random position in SHM, displacement is given as
x=Acos(wt), where A is the amplitude.

To find the equation for velocity at that point, you just derive it. The derivation of cos(x) is -sin(x). All is fine so far.

What I'm confused about is why the equation is x= -wAsin(wt), and not just
x= -Asin(wt). Where does the extra omega come from??

I've noticed that when you derive it again, you get w^2, so clearly it is multiplied by w each time, but I can't work out why.

I've asked a few people and nobody could explain it to me. No one is my class seems to have any idea either.

Any and all help is greatly appreciated. Thanks!
When you differentiate Acos(wt) you use the chain rule, which basically meant you multiply the derivative of cos(u) by the derivative of u, where u = wt here. Therefore you end up with -Asin(wt) x w = -Awsin(wt).
3. (Original post by solC)
When you differentiate Acos(wt) you use the chain rule, which basically meant you multiply the derivative of cos(u) by the derivative of u, where u = wt here. Therefore you end up with -Asin(wt) x w = -Awsin(wt).
Oh okay, thank you so much. I wouldn't have come up with that. I am yet to learn about differentiating trigonometric functions in Maths. It makes sense though.

Thanks again!

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: August 31, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### How to cope with a heavy workload

Poll
Study resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.