Pendulum and spring oscillation

  • Thread starter smhippe
  • Start date
  • #1
19
0

Homework Statement


A 5 kg sphere is connected to a thin
massless, but rigid rod of length L = 1.3 m to
form a simple pendulum. The rod is connected
to a nearby vertical wall by a spring with spring
constant k = 75 N/m, connected to it at a
distance h = 1.1 m below its point of
suspension. What is the angular frequency (in
rad/s) of the system for small amplitude
oscillations?


Homework Equations





The Attempt at a Solution


So I was listening to my teacher start to solve this problem. He starting talking about summing the torques between these two. I have the equation he wrote down from it, but I am not too sure what to do with it... ([tex]\tau[/tex])net = -Lmgsin[tex]\theta[/tex] - hk[tex]\Delta[/tex]xsin[tex]\beta[/tex] = m(l^2)[tex]\alpha[/tex]
Note: alpha is not a power...
I know that the small angle theorum makes sin go away. But how is beta and alpha related? And what about delta x? I don't know I've been working on it for a while and now I'm tired. Thanks for helping!
 

Answers and Replies

  • #2
kuruman
Science Advisor
Homework Helper
Insights Author
Gold Member
10,828
3,849
If you draw the drawing, you will see that you get two right triangles, one above the sphere and one below. They have a common right side that is Δx. Relate this side to L and θ using the top triangle and to h and β using the bottom triangle.
 

Related Threads on Pendulum and spring oscillation

Replies
16
Views
1K
Replies
33
Views
2K
  • Last Post
Replies
5
Views
6K
  • Last Post
Replies
10
Views
773
  • Last Post
Replies
5
Views
2K
Replies
12
Views
8K
  • Last Post
Replies
5
Views
898
  • Last Post
Replies
1
Views
6K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
2K
Top