Simple Harmonic Motion, Study notes of Physics

Download Simple Harmonic Motion and more Study notes Physics in PDF only on Docsity! Simple Harmonic Motion 04/13/23 - caused by a force thatis directly proportional to the displacement -displacementcenters around an equil position F,aX Example springs - Hooke's Law Es Isax 2Fy=0 m= 0.200kg x =constantofproportionality M Is =Fg x=0.068m R=spring constant (N/m) ↓ kx =mg ↑s = kX or -kx Fa k=M9 =6 9.8 = 28.8 0.68 Elastic Ep Calculate x for 0.500kg mass if K =28.8N/m v = Fs =kx =fg =mg kx =mg x =m =0.4m Example slingshot:takes 30.ON to stretch 1.0cm a) whatis up ofbands when 50.0g pulled back 0.20m b) whatspeed does itleave slingshot? a)fs=kx 30.0 =k(0.013k=3000N/mb) Ep=EA Us = k Vs =5kx2 =0.5(k) (0.2072 =605 Vs =Em = (0.050)v2 v=49m/s Displacement - is it) when the position is to the rightof the equil position (x=0) and (-) when located to the left -maxdisplacement =amplitude (A) velocity - is it) when moving to the rightand (-) when located to the left Acceleration (centr - direction ofstoringforce (ais (+) when Xis (-)) * is & max & end points, - f =ma= -kxor a= 0 & mid point Example 2.0kg hangs on end of spring, k =400N/m. mass displaced 12cm +released. Whatis the accel of the instanthe displacement is x = +1.0cm? a= +kx = your work done ·dtx a=x020) -Kx-work from spring a=- 14m/s2 Conservation of Energy 04/17/23 total mechanical energy (V+K) ofa vibrating system is constant -B V+k =EKA2 me ume x= Av=0 i X =-Ax=0 X=+A atany other point:V+ k = kx2+Emr2 v=f) (Energy:2Ex=1 = EeeEnter e Frequency frequency ofa wave is inverse of the period freq:#cycles/second I units:42 period -T= cycles frequency = 1 =" =I f =I SHM+UCM Xspring =Aware=Wcircle