Proving SHM using energy

  • Thread starter Mattofix
  • Start date
  • #1
138
0

Homework Statement



i have a bead on a wire shaped by y=cx^2 where y is the height - use conservation of energy to show that the system unfergoes simple harmonic motion. - no friction!

Homework Equations



I think to prove its SHM i need to get an equation in the form acc= - w^2 x

The Attempt at a Solution



KE + PE = A constant
1/2mv^2 + mgh = A constant
1/2mv^2 + mgcx^2 = A constant

... is this right? i am pretty sure i need it in the above form them from that i know what w is and can work out the period of this moyion.
 

Answers and Replies

  • #2
138
0
please help - with this i cant do the rest of the question :s
 
  • #3
144
0
Well as you said above, you need to show that the system satisfy an equation of the form acc = - constant * position.
More precisly something saying Z'' = - constant * Z. It doesn't matter what this constant exactly is, besides being a constant.
The v in your equation from the the kinetic energy is the SPEED of the bead so it's not the derivative of your x. What is v then? What happens if you plug that expression for v into your equation:

1/2mv^2 + mgcx^2 = constant

then taking the time derivative, so get something with dobbel derivative which is what you are seeking.
 
  • #4
138
0
what do i plug in for v? im totally confused...
 
  • #5
144
0
It's the length of the velocity vector, so it's
v^2 = x'^2 + y'^2
where x' and y' are the velocities in the x- and y- direction respectivly (ie time derivatives of x and y resp.). What is y' in this case?
 
  • #6
138
0
y' = 2xcx' ?
 
  • #7
138
0
ahhh -= please help somebaody - its in for tomrrow
 
  • #8
144
0

Related Threads on Proving SHM using energy

  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
4
Views
7K
  • Last Post
Replies
2
Views
16K
  • Last Post
Replies
2
Views
756
  • Last Post
Replies
8
Views
773
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
6
Views
7K
  • Last Post
Replies
5
Views
16K
Top