The values of mass m, spring constant k, dashpot resistance c, and force f(t) are given for a mass-spring-dashpot system with external forcing function. Solve the initial value problem and construct the graph of the position function x(t). mx" + cx' + kx = f(t), x(0)=x'(0) = 0 m = 1, k=64, c = 16; f(t) = 9t if 0 ≤t≤8, f(t) = 0 if t> 8 Solve the initial value problem. x(t)= Construct the graph of x(t). Choose the correct graph below. ○ A. 2- Ax 2 B. Ax ✓ Q ✓

145 S N Q-3 T. Brady Problem sy = Voy⋅ t + kayt 11 21 60f 1664/5² W w ½gt² + Vyt-sy = 0 at² + bt+C =0 Q-3 Hmwk #2

J Consider (Figure 1). Figure 10 ft 8 ft 8 ft 10 ft 16 A 6- FA-12 16 6 ft 1 of 1 > of 1 1 B 4 ft ▼ Part A Determine the projected component of the force F = 12 lb acting in the direction of cable AC. Express the result as a Cartesian vector. Express your answer in terms of the unit vectors i, j, and k. Use the 'vec' button to denote vectors in your answer. Express your answer in pounds to three significant figures. 195] ΑΣΦΗ Ivec FAC Submit Provide Feedback Request Answer D P Pearson a O PNING lb Next >

In Problem 28 nd the critical points and phase portrait of the given autonomous rst-order differential equation. Classify each critical point as asymptotically stable, unstable, or semi - stable. By hand, sketch typical solution curves in the regions in the xy - plane determined by the graphs of the equilibrium solutions dy/dx = ye^y-9y/e^

If you shake a magnetic compass e and then set it down, you can watch the needle bounce back and forth around its equilibrium position. If this motion is unimpeded by friction, it is an example of simple harmonic motion 2. You may learn more about simple harmonic motion in Phys 1230, but we'll be seeing another example soon in Unit 8. In this case, energy is being transferred continually between magnetic potential energy and kinetic energy, and the energy is conserved if there is no friction. When there is no kinetic energy, the needle is the maximally deflected and its magnetic potential energy is maximum; when the magnetic potential energy is minimum, the needle is moving the fastest. Conservation of energy shows that KE (0) +U (0) = Umax (functions of angle, not multiplication). For your compass, the measured angle between maximum deflection and equilibrium is 58°. What percent of the maximum kinetic energy does the needle have when it is only deflected 29° from equilibrium? Give…

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Take F= 250 N and d = 1.0 m (Figure 1). Figure 1.5 m B C A F 1 of 1 Determine the force in cable AC needed to hold the 19-kg ball D in equilibrium. Express your answer to three significant figures and include the appropriate units. ► View Available Hint(s) FAC = Submit Part B μA Value 1 Units ? Determine the force in cable AB needed to hold the 19-kg ball D in equilibrium. Express your answer to three significant figures and include the appropriate units. ▸View Available Hint(s)

For the mechanical system, use complex impedances to derive the transfer function matrix connecting the input forces ui and uz to the output displacements yı and y2 of the two point masses. Known are m, c, and k. Use a) matlab and b) Simulink to plot the displacements yı(t) and y2(t) of the mechanical system shown based on the transfer function matrix derived in that problem. Known are m = 1.2 kg, c =14 N s/m, and k=180 N/m. The input forces are u1= 50*e- 31*sin(16t) N and u2= 60/(t + 3) N. The initial conditions are zero. m m

An engineer wants to wind 10 turns of wire on a cylindrical rod. He/she measures the diameter of the rod to calculate using a mierometer to estimate the needed wire length. If the reading of the diameter is given in figure, calculate the required wire for 10 turns. 1 2 4 9. 10 Least significant bit= 0.05 mm, and zero error is 0. (Hint: 1 = 3, the length of the cylindrical bar is enough, and the windings do not overlap) A. 91.1 mm wire B. 83.7 mm wire C. 52.1 mm wire D. 62.4 mm wire E. 56.3 mm wire

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