Page 1. Physics 131: Lecture 22. SHM and Circles. Today s Agenda. Position. Velocity. Position and Velocity. Acceleration. v Asin.

Size: px

Start display at page:

Download "Page 1. Physics 131: Lecture 22. SHM and Circles. Today s Agenda. Position. Velocity. Position and Velocity. Acceleration. v Asin."

Roderick Fisher
5 years ago
Views:

1 Physics 3: ecture Today s enda Siple haronic otion Deinition Period and requency Position, velocity, and acceleration Period o a ass on a sprin Vertical sprin Enery and siple haronic otion Enery o a sprin orce pe on a rotatin turntable underoes periodic otion There is a close relationship between circular otion and siple haronic otion SHM and Circles Physics 0: ecture, P Physics 0: ecture, P Position Velocity nular position: t Call the vector pointin toward the pe The x-position o is x t This is our equation or SHM! The x-coponent o v is: v x v sin v r v sin t vax v t Physics 0: ecture, P 3 Physics 0: ecture, P 4 Position and Velocity cceleration t The x-coponent o a is: a x a a r a x v sin x is zero when v = + or - v is zero when x = + or - a t a ax t Physics 0: ecture, P 5 Physics 0: ecture, P 6 Pae

2 Siple Haronic Motion: x(t) = [](t) x(t) = []sin(t) v(t) = -[]sin(t) v(t) = [](t) OR a(t) () = -[ ](t) a(t) () = -[ ]sin(t) x ax = v ax = a ax = Period = T (seconds per cycle) Frequency = = /T (cycles per second) nular requency = = = /T Siple Haronic Motion: x(t) = [](t) v(t) = -[]sin(t) a(t) () = -[ ](t) x(t) = []sin(t) v(t) = [](t) a(t) = -[ ]sin(t) v t = 0 x= x ax = v= 0 t = 0 x= 0 v= v ax = Physics 0: ecture, P 7 Physics 0: ecture, P 8 Clicer Question : n 0.80 object is attached to one end o a sprin, and the syste is set into siple haronic otion. The displaceent o x o the object as a unction o tie is shown in the drawin. What is the correct equation or x? (a) x t (b) x 0.60 sin t (c) (d) x sin t x 0.60 sin t Physics 0: ecture, P 9 Clicer Question : Object is attached to sprin and is ovin in siple haronic otion. Object B is attached to sprin B and is ovin in siple haronic otion. The period and the aplitude o object B are both two ties the correspondin values or object. How do the axiu speeds o the two objects copare? a) The axiu speed o is one ourth that o object B. b) The axiu speed o is one hal that o object B. c) The axiu speed o is the sae as that o object B. d) The axiu speed o is two ties that o object B. e) The axiu speed o is our ties that o object B. Physics 0: ecture, P 0 Phase Constant Which one? Period or a Mass on a Sprin What can Newton s second law tell us about SHM? xt t x vt sin t v 0 sin v0 sin 3 x t t 3 Physics 0: ecture, P F a x a t t ω T Physics 0: ecture, P Pae

(a) 4 (b) (c) (d) / (e) /4 a) dd ore water to the lass. b) Reove soe water ro the lass.

3 Clicer Question.5: ass is attached to a sprin. I pull it distance o and it oscillates with requency. I I pull it a distance o what will the requency be? Clicer Question 3: Playin a tune on wine lasses is an application o SHM. To chane the requency o sound you need to adjust the aount o water. I you wanted to increase the requency, what would you do? (a) 4 (b) (c) (d) / (e) /4 a) dd ore water to the lass. b) Reove soe water ro the lass. Physics 0: ecture, P 3 Physics 0: ecture, P 4 Clicer Question 4: bloc o ass oscillates on a horizontal sprin with period T.0 s. I a second identical bloc is lued to the top o the irst bloc, the new period will be Clicer Question 4: bloc o ass oscillates on a horizontal sprin with period T.0 s. I a second identical bloc is lued to the top o the irst bloc, the new period will be. 0.0 s. B..4 s. C..0 s. D..8 s. E. 4.0 s. Physics 0: ecture, P 5 Physics 0: ecture, P 6 Clicer Question 5: Two identical blocs oscillate on dierent horizontal sprins. Which sprin has the larer sprin constant?. The red sprin. B. The blue sprin. C. There s not enouh inoration to tell. Clicer Question 6: ass on a sprin oscillates bac & orth with siple haronic otion o aplitude. plot o displaceent (x) versus tie (t) is shown below. t what points durin its oscillation is the total echanical enery (K+U) o the ass and sprin a axiu? (Inore riction). a) When x = + or - (i.e. axiu displaceent) b) When x = 0 (i.e. zero displaceent) c) The echanical enery o the syste is constant x + Physics 0: ecture, P 7 - Physics 0: ecture, P 8 t Pae 3

4 Enery Conservation I there are no non-conservative orces actin, the echanical enery will be conserved: E K U v x t axiu displaceent, x=, v = 0: E t zero displaceent, x = 0: ax E v E ω Physics 0: ecture, P 9 Enery Conservation This ay also be shown ore orally: E v x Find this as a unction o tie: sin t t E t t t t t t E sin E sin E sin Physics 0: ecture, P 0 Clicer Question 7: ass oscillates in siple haronic otion with aplitude. I the ass is doubled, but the aplitude is not chaned, what will happen to the total enery o the syste? a) total enery will increase b) total enery will not chane c) total enery will decrease Physics 0: ecture, P K Exaple bloc o ass 5.0 on a rictionless surace is attached to a horizontal sprin with = 3 N/. I the bloc is pulled 0.0 ro the equilibriu position o the sprin, what velocity will it have when it is 0.0 ro the equilibriu position? v K U K U i i vi xi v K i U U i x x i 0.44/s x 0.64J 50.44/s 0.64J 3N/ 0.0 3N/ 0.0 Physics 0: ecture, P Pendulu Motion Free-body diara or pendulu: T ω y x sin T Clicer Question 8: pendulu is hanin vertically ro the ceilin o an elevator. Initially the elevator is at rest and the period o the pendulu is T. Now the pendulu accelerates upward. The period o the pendulu will now be. reater than T B. equal to T C. less than T T Period and requency do not depend on, or! (For sall oscillations) Physics 0: ecture, P 3 Physics 0: ecture, P 4 Pae 4

Clicer Question 9: ass is suspended ro the ceilin o an elevator by a sprin. When the elevator is at rest, the period is T. What happens to the period when the elevator is acceleratin upward?

5 Clicer Question 9: ass is suspended ro the ceilin o an elevator by a sprin. When the elevator is at rest, the period is T. What happens to the period when the elevator is acceleratin upward? a) period will increase b) period will not chane c) period will decrease Vertical Mass and Sprin I we include ravity, there are two orces actin on ass. With ass, new equilibriu position has sprin stretched d. F y = 0 d = 0 d = / et this point be y = 0 F F = a (d - y) = a (/) - y = a - y = a Sae as horizontal! SHO Physics 0: ecture, P 5 New equilibriu position y = -d Physics 0: ecture, P 6 Proble bloc hans ro a sprin with sprin constant 000 N/. The bloc is pulled down 5.0 c ro the equilibriu position and iven an initial velocity o.0 /s bac towards equilibriu. What are the (a) requency, (b) aplitude and (c) total echanical enery o the otion? Physics 0: ecture, P 7 Pae 5

Page 1. Physics 131: Lecture 22. Today s Agenda. SHM and Circles. Position

Page 1. Physics 131: Lecture 22. Today s Agenda. SHM and Circles. Position Physics 3: ecture Today s genda Siple haronic otion Deinition Period and requency Position, velocity, and acceleration Period o a ass on a spring Vertical spring Energy and siple haronic otion Energy o