QUESTION 2 The vertical vibration at position i and at time t of a stretched homogeneous...
QUESTION 4 The vertical vibration at position r and at time t of a stretched homogeneous and infinitely long string is determined by the function u = u(x, y). Suppose that when the string is straight, it has a linear density of 2 and the tension at any given point of the string is 8. a. Derive the partial differential equation satisfied by u. b. If the initial position is 1 - r and the initial velocity is e 3...
Partial Differential Equation - Wave equation : Vibrating spring Question 2 A plucked string, Figure 2 shows the initial position function f (x) for a stretched string (of length L) that is set in motion by moving t at midpoint x =-aside the distance-bL and releasing it from rest timet- 0. f (x) bL Figure 2 (a) If the length of string is 10cm with amplitude 5cm was set initially, state the initial condition and the boundary conditions for the...
1,2 and 3 I. EXPERIMENT 1.10: STANDING WAVES ON STRINGS A. Abstract Waves on a string under tension and fixed at both ends result in well-defined modes of vibration with a spectrum of frequencies given by the formula below B. Formulas ē In=n (), n = 1,2,3,... v=JI where fn is the frequency of the nth standing wave mode on the string of length L, linear mass density , and under tension T, and v is the wave speed on...
6 (10) Spring Problems: (a) Find the displacement, y(t), (in arbitrary units) as a function of time for the mass in a mass-spring system described by the differential equatiorn Zy" 10y' + 8y = 100 cos 3t + 4et assuming that the mass is released from rest at the equilibrium position. (This forcing function is not very realistic.) (b) Assume the equation from part (a) describes a mass-spring-dashpot system with a dashpot containing honey. Imagine that the honey is changed...
a-d please 6 (10) Spring Problems: (a) Find the displacement, y(t), (in arbitrary units) as a function of time for the mass in a mass-spring system described by the differential equatiorn Zy" 10y' + 8y = 100 cos 3t + 4et assuming that the mass is released from rest at the equilibrium position. (This forcing function is not very realistic.) (b) Assume the equation from part (a) describes a mass-spring-dashpot system with a dashpot containing honey. Imagine that the honey...
Need Table F and how you do the calculations I. EXPERIMENT 1.10: STANDING WAVES ON STRINGS A. Abstract Waves on a string under tension and fixed at both ends result in well-defined modes of vibration with a spectrum of frequencies given by the formula below B. Formulas fn=n (*), n= 1, 2, 3,... v= T where fr is the frequency of the nth standing wave mode on the string of length L, linear mass density y, and under tension T,...
Question 2 ul lu (a) Find the solution u(x,t) for the 1-D wave equationfor -oo < x < oo with initial conditions u (x,0)-A(x) , where A(x) s presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and t, somewhat similar to f(x) on page 85 of the Notes Part 2. di+10 dı+15di+20 (b) Check for the wave equation in (a) that if f(xtct) (use appropriate value...
d1= 3 & d2= 2 Question 2 Find the solution 11(x, 1) for the 1-D wave equation aT = (a) 25-for -o <x < oo with initial conditions it (x,0) = A (x) , where A(x) is presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and 1, somewhat similar to fex) on page 8s of the Notes Part 2. 2 d2+5 r-0 di+10 di+15 di+20 3...
the question is in last picture. i provided the lab content... I need guidance. thank you. INVESTIGATION 10 ROTATIONAL MOTION OBJECTIVE To determine the moment of inertia I of a heavy composite disk by plotting measured values of torque versus angular acceleration. THEORY Newton's second law states that for translational motion (motion in a straight line) an unbalanced force on an object results in an acceleration which is proportional to the mass of the object. This means that the heavier...
mperial Valley College PROJECT #3 You may work in groups of up to 4 students. Each group turns in one homework, wnitten on separate paper e,aat in tiny writing on this sheetl with llwri and all stens shoan doack All students in each group recee the same grade This assignment is due ot the begrring 덱 dass on"huidey July 27 (day of Find Exon This project is worth o total f 40points Homework will be graded not only on correctness,...