

Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
The spring is neither stretched nor compressed. (b) The object is displaced and the spring is stretched. • When the restoring force is directly proportional to ...
Typology: Lecture notes
1 / 3
This page cannot be seen from the preview
Don't miss anything!
Created by: Binh Cao
o Angular frequency (ω): 𝜔 = 2 𝜋𝑓 = !! ! (rad/s) A/ Ideal spring 𝐹!"#$%!&'( = −𝑘𝑥
Created by: Binh Cao k: spring constant x: displacement from equilibrium 𝜔 = ! !
! !!
! !! ! !
! !
!! !
! ! 𝑥 = 𝐴 cos(𝜔𝑡 + 𝛷) Φ: initial angular displacement 𝐸 = ! !
! !
! !
E: mechanical energy of the system 𝑣!: velocity of mass m at x (m/s) B/ Simple pendulum 𝐹!"#$%!&'( = −𝑚𝑔𝑠𝑖𝑛𝜃 ≅ −𝑚𝑔𝜃 (when θ is small) Θ: angular displacement form equilibrium 𝜔 = ! !
! !!
! !! ! !
! !
!! !
! ! L: string length (m) C/ Examples 1/ When a body of unknown mass is attached to an ideal spring with force constant 120 N/m, it is found to vibrate with a frequency of 6.00 Hz. Find (a) The period of the motion; (b) The angular frequency; (c) The mass of the body. Solution: k = 120 N/m; f = 6.00 Hz (a) 𝑇 = ! !
! !.!!
(b) 𝜔 = 2 𝜋𝑓 = 2 𝜋× 6. 00 = 37. 7 (rad/s) (c) 𝜔 = ! ! or 𝑚 = ! !!^
!"# !".!!^