Question

Physics 220 Homework #12 Handout Name: Lab Section # Staple this page to the front of Homework #12. For periodic motion of a mass oscillating due to a spring, we have demonstrated that the position of a mass as a function of time has the following form: (1) Acos (or + y) where o = sqrt (k/m) What does A represent physically? What are the units of A? What does o represent physically? What are the units of w? What does o represent physically? What are the units of o? cof+ o)? What does (cf + ) represent physically? What are the units of (i.e. what does it mean if (of+ o) = 2x at a particular time t-T? The equation at the top gives you the position of the mass as a function of time. What would you need to do to find the velocity of the mass as a function of time? (remember dx/dt = v). Perform that calculus derivative and write the equation that describes the mass's velocity as a function of time here (don't forget the chain rule): Now that you have the velocity, what would you do to calculate the acceleration of the mass as a function of time? Perform that step and write the equation that describes the mass's acceleration as a function of time here: How does the equation of the acceleration compare to the equation for the position? A sign difference is important here ... what does the sign mean physically?

Answer 1

ut cas (cut-0) A depresents the more displacement from the mean position, s. C, amplitude. Its unit is m. w represents the angular velocity of the mass its unit es rad see & is the initial phase of the moss, ie; how much the mass was away from or behind the mean. position at time to. Its unit is radian We know u= du at So ved (A cas lent-b alt - & A sus funt-6) of (cut-0) Toa - A sis (uet-d) w ar du (-Awais cent - 0] a- 04 - Aw car (art-1) a (cut-o) - Aw cos(ut-d). w a =- Awe confent-6) a wos (x- Acos(ut-07 : a a a but ve sign shows that it is directed motion of the particle - Chosite to the