4.A mass of 5 kg stretches a spring 10 cm. The mass is acted on by an external force of 10 sin(t/2) N (newtons) and moves in a medium that imparts a viscous force of 2 N when the speed of the mass is 4 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 3 cm/s, formulate the initial value problem describing the motion of the mass.

Q: 22.In the absence of damping, the motion of a spring–mass system satisfies the initial value problem…

A:

Q: 1. An undamped spring-mass system with mass m = 2 and a spring constant k = 8 is suddenly set in…

A: Solution in step 2

Q: Suppose heat is lost from the lateral surface of a thin rod of length L into a surrounding medium at…

A: The heat equation given is as follows: k∂2u∂x2-hu=∂u∂t, 0<x<L,…

Q: [3] Consider the equation for free mechanical vibration, my" + by' + ky = 0 and assume the motion is…

A: Given equation is, my''+by'+ky=0 So, the auxiliary equation of the given equation is,…

Q: 5. A 1/4-kg mass is attached to a spring whose stiffness constant is 8 N/m. The damping constant for…

A:

Q: A 10-kg mass is attached to a spring having a spring constant 140 N/m. The mass is started in motion…

A: To determine the initial value problem, consider the spring mass system as shown in the figure;…

Q: Given the differential equation of the family of circles with radius of 2 units and whose center's…

A:

Q: A cylindrical tank initially contains 400 liters of fluid with 90 grams of salt dissolved in it.…

A: NOTE: Refresh your page if you can't see any equations. . y=amount of salt at time t

Q: This is a differential equations problem.

A:

Q: What is the amount of work done on a spring when it is compressed from its natural length of 1 meter…

A: Topic = Algebra

Q: For a 1 kilogram mass on a spring with spring constant k = 4 N/m and resistance of 4 times the…

A:

Q: A mass weighing 4 lb stretches a spring 2 in. Suppose that the mass is given an additional 6-in…

A: mg = weight =4 lb; L = initial displacement = 2 in = 2/12 = 1/6 feet; Fdampening = Viscous…

Q: When a mass of 2 kilogram is attached to a spring whose constant is 32 n/m, it comes to rest in the…

A:

Q: A spring with spring constant k = 0.6 N/m has an equilibrium length of 1.7 m. How much work is…

A: To determine the energy stored in the spring.

Q: A mass weighing 6 Ib stretches a spring 3.5 inches. The mass is given a positive displacement of 5…

A: The weight w will be 6 lb and the length of the spring (L) is 3.5 inch which will be 3.512ft. The…

Q: Specifically a DiffEq problem. Question in pic below. Answer: (1/16)pi(2n+1), n = 0, 1, 2, ...

A:

Q: 3. A spring with an m-kg mass and a damping constant 9 can be held stretched 1 meters beyond its…

A:

Q: A 4-pound weight is hung on a spring and stretches it 1 foot. The mass spring system is then put…

A: Draw the figure, which is given below. In equilibrium,  mg−kx0=0⇒mg=kx0 Given, mg=4 and x0=1…

Q: A 16-lb weight is attached to the lower end of a coil spring sus-pended from the ceiling and having…

A:

Q: A 2 kg mass is attached to a spring with spring constant k = 200 N/m. The mass is displaced 2/3…

A: Answer is mentioned below As mentioned, have provided the solution for d and e

Q: What is the amount of work done on a spring when it is compressed from its natural length of 1 meter…

A: Using formula work done W=1/2kx2 where k =spring constant and     x=displacement in spring by…

Q: A cylindrical tank initially contains 400 liters of fluid with 90 grams of salt dissolved in it.…

A:

Q: A 1-kilogram mass is attached to a spring whose constant is 21 N/m, and the entire system is then…

A:

Q: A 1-kilogram mass is attached to a spring whose constant is 27 N/m, and the entire system is then…

A:

Q: A 1-kilogram mass is attached to a spring whose constant is 18 N/m, and the entire system is then…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: What mass of water at 26.0°C must be allowed to come to thermal equilibrium with a 1.90-kg cube of…

A: Note that, the specific heat of aluminum is 900 J/kg·°C and the specific heat of water is 4186…

Q: A 1-kilogram mass attached to a spring whose constant is 18 N/m, and the entire system is then…

A:

Q: if the mass is initially released from a point 1 meter below the equilibrium positon with an upward…

A: We will find the equation of motion as shown below

Q: A mass weighing 32 pounds stretches a spring 8 feet and an impressed force f(t) = e-2t sin t acts on…

A: Consider the provided question, Given,  32 pound weight stretches a spring 8 feet.

Q: Consider the initial value problem my" + cy' + ky = F(t), y(0) = 0, y'(0) = 0 modeling the motion of…

A: Please be careful when typing

Q: Consider a driven oscialting spring-mass system modeled by my'' + by' + ky = Fo cos(wt). Find the…

A: Given: m=5kg K=10 N/M C=5Nsm Natural frequency ωn=km=105=2=1.4142 Critical damping coefficient…

Q: Estimate the value of 217(1/3) a. approximation b. differentials

A:

Q: A 1-kilogram mass is attached to a spring whose constant is 27 N/m, and the entire system is then…

A: .

Q: 1 A spring is such that a 4-lb weight stretches it 6 in. An impressed force; -cos8t is acting on the…

A: We have to determine the position of the weight as a function of time x(t).

Q: When a mass of 2 kilograms is attached to a spring whose constant is 32 N/m, it comes to rest in the…

A:

Q: 3.A mass of 100 g stretches a spring 5 cm. If the mass is set in motion from its equilibrium…

A:

Q: nass weighing 32 Ib is attached to a spring hanging from the ceiling and comes to rest at its…

A: The objective of this problem is to find the equilibrium solution of spring attached with an…

Q: A spring with spring constant k = 5 N/m has an equilibrium length of 0.8 m. How much work is…

A: Given that k= 5 N/m So, F(x)=kx=5x We will have to stretch the spring (1.1-0.8)=0.3 m from its…

Q: Two particles A and B, of masses 0-3 kg and 0-7 kg, are moving towards each other on a smooth…

A: Given that masses of particles are                                                      mA=0.3…

Q: A 10 kg weight is attached to a spring with constant k = 160 kg/m and subjected to an external force…

A:

Q: A 1-kilogram mass is attached to a spring whose constant is 21 N/m, and the entire system is then…

A: Given that a 1-kilogram mass is attached to a spring whose constant is 21 N/m, and the entire system…

Q: 6. A 2 kg mass is attached to a spring with spring constant k = 200 N/m. The mass is displaced 2/3…

A: We form an ordinary equation my" = -kx

Q: 1st Case (IBVP Summary) 1.3uxx, 0 0 u(0, t) = 70°F, u(5ft, t) = 150°F, t > 0 u(x,0) = 60°F, 0 < x <…

A:

Q: A spring with constant k = 2 is suspended in a liquid that offers a damping force numerically equal…

A:

Q: Suppose that a mass of 219 g stretches a spring 5 cm. If the mass is set in motion from its…

A:

Q: A 1-kilogram mass is attached to a spring whose constant is 24 N/m, and the entire system is then…

A: Given m=1,k=24,β=11 The general equation of motion for a spring mass system with damping is,…

Q: 3. A model for the velocity v at time t of a certain object falling under the influence of gravity…

A: The equation of the certain object in viscous medium is given by dv/dt = 1 - v/8

Q: Write the differential equation that governs the motion of the damped mass-spring system, and find…

A:

Q: 4.1. Derive the heat equation with a metal rod with variable cross-sectional area A(x). Using the…

A: Cross section area of metal rod is Ax. Energy density per unit volume is hx,t. Energy in the…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.