{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Midterm_1_EQ - L x ae è ø cos w n t f n n = np L T...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics 1B MIDTERM 1 Kyle Chin Simple Harmonic Motion F spring = - kx M d 2 x dt 2 = - kx x ( t ) = A cos[ w 0 t ] x ( t ) = B sin[ w 0 t ] or F total = - Mg + kd d 2 x dt 2 = - w 0 2 x x ( t ) = A cos[ w 0 t ]+ B sin[ w 0 t ] x ( t ) = x (0)cos[ w 0 t ]+ v (0) w 0 sin[ w 0 t ] A = x (0) B = v (0) w 0 ϖ 0 2 = k M T = 2 p w 0 f = 1 T Conservation of Energy : 1 2 Mv 2 + 1 2 kx 2 = 1 2 kx max 2 Pendulum θ ( t ) = q (0)cos[ w 0 t ]+ ú q (0) w 0 sin[ w 0 t ] d 2 q dt 2 = - g l sin q ϖ 0 = g l T = 2 p l g f = 1 2 p g l Damped Oscillations F D = - bv M d 2 x dt 2 = - b dx dt - kx d 2 x dt 2 + n dx dt + w 0 2 x = 0 ϖ 0 2 = k M ν = b M x ( t ) = x 0 e - gt cos w d t γ = ν 2 ϖ d 2 = w 0 2 - n 2 4 t damp = 1 g (i) overdamping ϖ 0 < n 2 no oscillations (ii) critical damping ϖ 0 = n 2 no oscillations; fastest decay (iii) underdamping ϖ 0 > n 2 oscillations (decreasing amplitude) Driven Oscillations M d 2 x dt 2 = - b dx dt - kx + F 0 cosW t d 2 x dt 2 + n dx dt + w 0 2 x = a 0 cosW t 1
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
ν = b M ϖ 0 2 = k M a 0 = F 0 M = forcing angular frequency x ( t ) = x P ( t ) + x H ( t ) where x H ( t ) dies away over time x P ( t ) = K cos[W t + d ] K = a 0 ( w 0 2 - W 2 ) 2 + n 2 W 2 δ = tan - 1 - n W w 0 2 - W 2 æ è ç ö ø ÷ K is maximized when max = w 0 2 - n 2 2 Q (quality) factor Q = w 0 w » w 0 n w = width at K max 2 higher Q = sharp peak Waves – STANDING z ( x , t ) = A sin( kx )cos( wt ) kl = 2 p ϖ = kv v = fl T P = 2 p w L = nl 2 k = np L f n = nf
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: L x ae è ç ö ø ÷ cos( w n t + f n ) n = np L T m f n = n 2 L T m T P = 1 f Wave Equation μ ∂ 2 z ¶t 2 = T ¶ 2 z ¶x 2 2 z ¶t 2 = v 2 ¶ 2 z ¶x 2 – TRAVELING Equation for a moving point: x = x + vt Wave speed v = ± T m = kv T P = l v = 2 p w k = 2 p l f = v l z ( x , t ) = z sin[ k ( x ± vt )] = z sin[ kx ± wt )] +v : moving right-v : moving left In general z ( x , t ) = z sin kx cos wt = 1 2 z sin( kx + wt ) + sin( kx-wt ) { } = F ( kx + wt ) + G ( kx + wt ) 2...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern