Static Equilibrium Lab

Question 27 Three particles of mass m, 4m and 4m are constrained to move along a frictionless horizontal groove. The first two particles are connected by a spring of stiffness k and natural length lo. The last two particles are connected by a spring of stiffness 2k and natural length lo. Initially the particles are in equilibrium at points A, B and C and we measure the displacements x, y and z of the three particles from these equilibrium points, as shown in the following diagram. m X 4m k, lo mrrrrrrrrr mmmmmmmm The system is displaced from equilibrium and we are concerned with modelling the subsequent motion. Z (a) Draw a force diagram for each particle, showing all of the forces acting on the particles. (b) Determine the changes in spring forces from their equilibrium values in terms of the above variables and parameters. 2k, lo 4m BY (c) Derive the equation of motion of this mechanical system in the form = A X y 2 where A is a matrix that you should specify explicitly. (d) Show…

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The hanging mobile pictured above consists of two masses, m1 and m2, suspended from a uniform 10 cm long rod, which is in turn suspended from the ceiling at an angle of 70 as pictured above. The mass m1 is 0.02 kg, while the mass of the rod is mr = 0.01 kg. Assuming the mobile is in a state of static equilibrium, find the value of mass m2.

a) In periodic motion, it is often interesting to investigate the harmonic motion of an object. The decrease in amplitude caused by dissipative force is called damping, and the corresponding motion is called damped oscillation. Damped oscillation is governed by the following equation, where is the angular frequency of oscillation, A is the initial amplitude of the oscillation, m is the mass of an object, b is a constant that describes the strength of the damping force, t is time in seconds, h is the ratio between a force constant k and the mass m: where x(t) = Ae sin(at + p) If = 60°, A = 4, v = 2m @= h b² 4m² b = 0.25, create a plot x(t) for 0≤t≤ 15, with h = 4. Label all the axes, 2m include gridlines and provide a title in your plot.

Note:  Please provide a detailed, step-by-step handwritten solution (no explanations) created entirely without AI involvement. The work must reflect expert-level precision, as I will assess and rate it based on accuracy and quality. Ensure every calculation is thoroughly double-checked before submitting. Question: In Figure 6, a 2-kg block is subjected to a harmonic force F = 30 cos 5t. Given that if k1 = 40 N/m, k2 = 60 N/m, k3 = 76N/m, and c = 50 N.s/m, derive the equation describing its steady-state motion.

1. The development of thermodynamics since the 17th century, which was pioneered by the invention of the steam engine in England, and was followed by thermodynamic scientists such as Willian Rankine, Rudolph Clausius, and Lord Kelvin in the 19th century. explain what the findings or theories of the 3 inventors are! Please answer fast max 25-30.minutes thank u

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Thermodynamics - need help with part a and b

THERMODYNAMICS: Mollier Diagram: Steam Table Using the Steam Table below, find Δhf and Δhg in BTU/lbm and Δsf and Δsg in kJ/kgm-K and for the following parameters: P1 = 9.5 kgf/cm2  P2 = 15 kgf/cm2 With step by step explanation pls NOTE: This table uses SI unit as stated below: Pressure: MPa Temperature: °C Internal Energy and Enthalpy: kJ/kgm Entropy: kJ/kgm-K

Hello I have two pictures with some questions Id like to get answers to! Short and great explanations please thank you !

1. In the laboratory, when you hanged 100 grams at the end of the spring it stretched 10 cm. You pulled the 100-gram mass 6 cm from its equilibrium position and let it go at t = 0. Find an equation for the position of the mass as a function of time t. 2. The scale of a spring balance found in an old Physics lab reads from 0 to 15.0 kg is 12.0 cm long. To know its other specifications, a package was suspended from it and it was found to oscillate vertically with a frequency of 2.00 Hz. Calculate the spring constant of the balance? (b) How much does the package weigh?

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950g static mass Static Force Exerted by the Spring   Time to Complete 60 Revolutions 39 sec Angular Velocity of the Rotating Mass   Radius of Rotation for the Rotating Mass .179 m Mass of the Rotating Mass . 449 kg Centripetal Force Exerted on the Rotating Mass   % Difference Between the Static and Centripetal Forces

3) A thin rod of mass m and length / is balancing vertically on a smooth horizontal surface. The rod is disturbed slightly and falls to the right. Using the angle between the ground and rod as your generalized coordinate, derive the equations of motion using both the Newton-Euler approach (F=ma) and Lagrange's equations. Show that the solutions are the same. Answer: m,l 1 m1² (3cos²0 + 1)-ml²6² cosesine +mglcose = 0 rod