Problem 9. Consider a horizontal mass-spring system with mass 10 kg and spring constant 10 N/m. a. If the surface the mass slides on is frictionless and there are no external forces, setup and solve the model for the position of the spring as a function of time. See the last page of this review for relevant eigenvalues and eigenvectors. b. Suppose the force due to friction is proportional to the velocity of the mass with proportionality constant 20 Ns/m. Setup and solve the new model for the position of the spring as a function of time. See the last page of this review for relevant eigenvalues and eigenvectors. c. Is the mass-spring system calculated in part b underdamped, critically damped, or overdamped? Explain your reasoning.

Fundamental.7 deals with the equation of motion. The use of the equation of motion to solve this problem is mandatory. Solution using other approaches (conservation of energy ...) will be automatically considered false. For the problem related to Fundamental.7 sketches of the system showing: • the respective velocity and acceleration and the frame of reference considered • the forces acting on the system of considered, in other words, a free body diagram (FBD) are mandatory. Their absences will automatically make the problem false. B The pendulum bob B has a weight of 3lb and is released from rest in the position shown, 0 =0°. Determine the tension in string BC of length r = 4 ft at the instant the bob reaches point D, =4°.

Needs Complete typed solution with 100 % accuracy.

diagram, F, is the input force exerted on the cart by the voltage applied to the motor, m, is the mass of the cart. The encoder is used to keep track of the position of the cart on the track. Cart Encoder Mater March 7, 2023 Track X Figure 5: Free body diagram of the cart (ignoring friction) Using Figure 5 and basic Newtonian dynamics you can derive the equations governing the system. 3.3 Motor Dynamics The input to your system is actually a voltage to the cart's motor. Thus, you need to derive the dynamics of the system that converts the input voltage to the foren exertal on the cart. These are the dynamics of the motor. Figure 6 shows a diagram of the electrical components of the motor. Figure 6: Clasic armature circuit of a standard DC motor For this derivation of the motor dynamics we assume the following: • We disregard the motor inductance: IR, so we can use the approximation 0. • Perfect efficiency of the motor and gearbox: -- 1. The torque generated by the motor is proportional…

The ideal gas law, discovered experimentally, is an equation of state that relates the observable state variables of the gas--pressure, temperature, and density (or quantity per volume): PV = NkBT (or pV = nRT), Figure L₂ Lx 1 of 1 Part A Find the magnitude of the average force (F) in the x direction that the particle exerts on the right-hand wall of the container as it bounces back and forth. Assume that collisions between the wall and particle are elastic and that the position of the container is fixed. Be careful of the sign of your answer. Express the magnitude of the average force in terms of m, vr, and L₂. ► View Available Hint(s) Submit Part B IVE ΑΣΦ ? Imagine that the container from the problem introduction is now filled with N identical gas particles of mass m. The particles each have different x velocities. but their average x velocity squared. denoted

Data has been gathered from a lifting system used to transport engine parts. The system consists of a drum and cable. The following data was obtained when the drum lowers the load (assume constant acceleration). Drum diameter = 0.8m Mass of load = 3kg Initial velocity = 0 m/s Time to descend = 0.5 secs Distance travelled = 0.25m You have been asked to use this information to determine: The final linear velocity of the load The linear acceleration of the load The final angular velocity of the drum The angular acceleration of the drum The tension force in the cable The torque applied to the drum   In determining the above quantities, you should clearly state the formulae used and apply dimensional analysis techniques to show that all values/units used are homogeneous.   From the formulae used (above) you should apply dimensional analysis techniques to develop two equations for power (in terms of linear velocity and angular velocity).

Multiple DOF SystemsA 2-D spring-mass, frictionless system has the following parameters:m1 = 72m2 = 27k1 = 381k2 = 183x1,0 = 0 mx2,0 = 1 mv1,0 = -1 m/sv2,0 = 0 m/s  In MATLAB, solve numerically for x1(t) and x2(t).

Using the equation of motion and please include free body diagram. thank you!

Please solve with steps

6.2Build code to satisfy, please.