An object of mass 3 grams hanging at the bottom of a spring with spring constant 2 grams per second square is moving in a liquid with damping constant 3 grams per second. Denote by y vertical coordinate, positive downwards, and y = 0 is the spring-mass resting position. (a) Write the differential equation y" = f(y, y) satisfied by this system. f(x, y) = Note: Write t for 1, write y for y(t), and yp for y' (t). (b) Find the mechanical energy E of this system. Σ Σ E(1) = Note: Write t for 1, write y for y(1), and yp for y' (t). (c) Find the differential equation E' = F(y) satisfied by the mechanical energy. F(y) = Σ Note: Write t for 1, write y for y(1), write yp for y' (t), write E for E(t).

An object of mass 3 grams hanging at the bottom of a spring with spring constant 2 grams per second square is moving in a liquid with damping constant 3 grams per second. Denote by y vertical coordinate, positive downwards, and y = 0 is the spring-mass resting position. (a) Write the differential equation y" = f(y, y) satisfied by this system. f(x, y) = Note: Write t for 1, write y for y(t), and yp for y' (t). (b) Find the mechanical energy E of this system. Σ Σ E(1) = Note: Write t for 1, write y for y(1), and yp for y' (t). (c) Find the differential equation E' = F(y) satisfied by the mechanical energy. F(y) = Σ Note: Write t for 1, write y for y(1), write yp for y' (t), write E for E(t).

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: A BMW vehicle consumes 2.5 gallons of gasoline in 60 minutes while operating at3000 RPM. Calculate…

A: Given:The BMW vehicle consumes gallons of gasoline in minutes.Each gallon of gasoline contains of…

Q: The sprinter begins from rest at position A and accelerates along the track. If the stationary…

A: Given: Sprinter begins from A to O = 42 m distance from sprinter to O parallel to the track = 19 m…

Q: An engine turns at 250 revolutions per minute and its stroke is 450 mm. Find the average piston…

A: Step 1: (1). Average Piston Speed: The formula for the average piston speed is: Average Piston…

Q: The following figure shows a journal bearing supports a radial load of 10 kN at speed of 2400 RPM.…

Q: JC BRA JC Ma = 2.5kg BRD BAD Mb=7kg Given that: The line of force for BRD is 5cm. Distance JC to Ma…

A: Mass, Ma= 2.5 kg Distance between JC and Ma, a= 16 cm Mass,Mb= 7 kg Distance between JC and Mb, b=…

Q: Is this definitely correct? A few calculators online such as BMEP calculators give me a different…

A: Given data:Torque = T = 100 NmEngine is four stroke,so there is one power stroke after two…

Q: Rc is -178.25 Ib. Why in the formula it's 17825 ?

A: The value of RC is represented as : Rc=-178,25 =-17825 lb The negative sign denote the direction…

Q: Please help. Written on paper not typed on computer or keyboard please. Need help on both…

A: Approach to solving the question: Detailed explanation:Examples: Key references:

Q: An angular velocity of 50 rad/s expressed is approximately .. (rpm =revolutions per minute) O 100r…

A: Calculated rpm ( revolution per minute).

Q: To find the Mechanical Advantage of ANY simple machine when given the force, use MA = R/E. An Effort…

A: Write the value of load. R=90 N Write the value of effort. E=30 N

Q: are you sure it's not c?, can you show with diagrams

A: Given Data: To Find: Chose the correct option/s.

Q: Find the volume of the propane tank. Assume IPS units, set before you begin to sketch the part.. The…

Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

Fast pls solve this question correctly in 5 min pls I will give u like for sure Sini.

An object of mass 3 grams hanging at the bottom of a spring with a spring constant 2 grams per second square moving in a liquid with damping constant 3 grams per second. Denote by y vertical coordinate, positive
downwards, and y = 0 is the spring-mass resting position.
(a) Write the differential equation y" = f(y, y) satisfied by this system.
f(x, y) =
Note: Write t for t, write y for y(t), and yp for y' (t).
(b) Find the mechanical energy E of this system.
E(t) =
Note: Write t for 1, write y for y(t), and yp for y' (t).
(c) Find the differential equation E' = F(y) satisfied by the mechanical energy.
F(y) =
Σ
Note: Write t for 1, write y for y(t), write yp for y' (t), write E for E(t).
Σ

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given data;

VIEW

Step 2: Mechanical Energy;

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 9 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

6. The electro-mechanical system shown below consists of an electric motor with input voltage V which drives inertia I in the mechanical system (see torque T). Find the governing differential equations of motion for this electro-mechanical system in terms of the input voltage to the motor and output displacement y. Electrical System puthiy C V V₁ R bac (0) T bac T Motor - Motor Input Voltage - Motor Back EMF = Kbac ( - Motor Angular Velocity - Motor Output Torque = K₂ i Kbacs K₁ - Motor Constants Mechanical System M T Frictionless Support
Damped Oscillatory Motion The setup consists of a mass m and a mass ", connected by a massless string of length { via a massless pulley. There is no friction between the string and the pulley. Mass m/2 is connected to a spring (spring constant k) and to a damper, damping constant b. Write down the equation of motion for the mass m. Use the coordinate x, with x = 0 being the equilibrium position of the system. Question т m/2] k b
A 25 kg mass is attached to a spring with spring constant 100 N/m. The mass is driven by an external force equal tof(t) = 5 cos(2t). The mass is initially released from rest from a point 1 m below the equilibrium position. (Use theconvention that displacements measured below the equilibrium position are positive.) Write the initial-value problem which describes the position of the mass.
solve by assuming a value of ζ of 0.5 and plot X/Y vs r and then solve for K and C based on r and ζ. Then plot using the given MATLAB code
Consider the double mass/double spring system shown below. - click to expand. Both springs have spring constants k, and both masses have mass m; each spring is subject to a damping force of Ffriction -cz' (friction proportional to velocity). We can write the resulting system of second-order DEs as a first-order system, t' (t) = Au(t), with = (₁, 21, 22, 2₂) I For values of k = 4, m = 1 and c = 1, the resulting eigenvalues and eigenvectors of A are -0.039-0.248i 0.813 A₁2=-0.5±3.2i, v₁ = 0.024 +0.153i -0.502 -0.134-0.302i 0.409 -0.2160.489 0.661 (a) Find a set of initial displacements (0), 2(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. A3,4 -0.5± 1.13i, z = and (2₁ (0), ₂(0)) = Enter your answer using angle braces, (and). (b) At what frequency will the masses be oscillating in this mode? Frequency rad/s
Solve all parts or skip it
3. A 100-pound weight is suspended from a vertical spring whose module is 100 pounds per foot. The weight is pulled downward 9 inches from its equilibrium position and released. Viscous fluid exerts 20 Ibs of force when the plunger moves through it at 0.5 ft/sec; 3.a What is the damping condition? Write the equation which describes the motion of the weights. Show graph. 3.b displacement 3.c velocity 3.d acceleration
attached is a past paper question in which we werent given the solution. a solution with clear steps and justification would be massively appreciated thankyou.
A mass m = 4 kg is attached to both a spring with spring constant k = 197 N/m and a dash-pot with damping constant c = 4 N-s/m. The mass is started in motion with initial position To = 2 m and initial velocity vo = 8 m/s Determine the position function z(t) in meters. r(t) = Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form z(t) = C₁e-pt cos(w₁ta₁). Determine C₁,w₁a₁ and p. C₁₂ = W₁ = -α₁ = P= Graph the function z(t) together with the "amplitude envelope" curves * = C₁e-Pt and x = C₁e-pt Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected (so c = 0) Solve the resulting differential equation to find the position function u(t). n this case the position function u(t) can be written as u(t) = Cocos(wotao). Determine Co, wo and co Co Po (assume 0 a₁ < 2π) 20 (assume 000 < 2π) inally graph both function (t) and u(t) in the same window to illustrate the effect…
2. A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position xo and initial velocity vo. Find the position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the form x(t)=C₁e Pt cos (@₁t-a₁). Also, find the undamped position function u(t)= Cocos (@ot-ao) that would result if the mass on the spring were set in motion with the same initial position and velocity, but with the dashpot disconnected (so c = 0). Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t). 1 m = 2, c = 4, k = 6, x₁ = 4, V₁ = 0 x(t) = which means the system is (1). (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than or…
5. A mass m is attached to both a spring (with given spring constant k) and a dashpot (with damping constant c). The mass is set in motion with initial position xo and velocity vo. A) Find the damped position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the formx(t) = ce¬pt cos(wit – a1) B) Find the undamped function u(t) = coe-pt cos(@ot – ao) that would result if the mass on the spring were set in motion with the same initial position and velocity but with the dashpot disconnected. m = 3, c = 30, k = 63, xo = 2, vo = 2
4 QUESTION 20 The car bridge in Figure Q20 can be modelled as a damped-spring oscillator system with mass M = 10000 kg, spring coefficient k = 50000 N-m-1 and damping constant c = 50000 N-s-m-1. Cars cross the bridge in a periodic manner such that the bridge experiences a vertical force F (N) expressed by F = mg sin(10t) where m = 1136 kg is the average mass of passing cars, g = 9.81 m-s-2 is the gravitational acceleration and t (s) is the time. Determine the maximum force magnitude transmitted to the foundation (see Figure Q20) during the steady-state oscillatory response of the system. Provide only the numerical value (in Newtons) to zero decimal places and do not include the units in the answer box. E m M foundation Figure Q20: Vibrating car bridge.