Question

Suppose the motion of a weight attached to a spring is given by the differential equation...

Suppose the motion of a weight attached to a spring is given by the differential equation

y′′+ 6y+ 10y= 0

and

y(0) = 0, y′(0) = 3. Find the solution y(t) to this initial value problem.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
. Write and solve a differential equation that models the motion of a spring whose mass...
. Write and solve a differential equation that models the motion of a spring whose mass is 2a, spring constant b, and damping a, where the numbers a is 3, b is 6. Assume that the initial position is y = 1 and initial velocity is y 0 = −1. Write your solution as a single, phase-shifted cosine function.
find the general solution of the given differential equation 1. y''−2y'+2y=0 2. y''+6y'+13y=0 find the solution...
find the general solution of the given differential equation 1. y''−2y'+2y=0 2. y''+6y'+13y=0 find the solution of the given initial value problem 1. y''+4y=0, y(0) =0, y'(0) =1 2. y''−2y'+5y=0, y(π/2) =0, y'(π/2) =2 use the method of reduction of order to find a second solution of the given differential equation. 1. t^2 y''+3ty'+y=0, t > 0; y1(t) =t^−1
Find an equation of the curve that passes through the point and has the given slope....
Find an equation of the curve that passes through the point and has the given slope. (Enter your solution as an equation.) (0, 4), y' = x 6y 2. Find the particular solution of the differential equation that satisfies the initial condition. (Enter your solution as an equation.) Differential Equation Initial Condition y(1 + x2)y' − x(7 + y2) = 0 y(0) = 3
MASS SPRING SYSTEMS problem (Differential Equations) A mass weighing 6 pounds, attached to the end of...
MASS SPRING SYSTEMS problem (Differential Equations) A mass weighing 6 pounds, attached to the end of a spring, stretches it 6 inches. If the weight is released from rest at a point 4 inches below the equilibrium position, the system is immersed in a liquid that offers a damping force numerically equal to 3 times the instantaneous velocity, solve: a. Deduce the differential equation that models the mass-spring system. b. Calculate the displacements of the mass ? (?) at all...
MASS SPRING SYSTEMS problem (Differential Equations) A mass weighing 6 pounds, attached to the end of...
MASS SPRING SYSTEMS problem (Differential Equations) A mass weighing 6 pounds, attached to the end of a spring, stretches it 6 inches. If the weight is released from rest at a point 4 inches below the equilibrium position, and the entire system is immersed in a liquid that imparts a damping force numerically equal to 3 times the instantaneous velocity, solve: a. Deduce the differential equation that models the mass-spring system. b. Calculate the displacements of the mass ? (?)...
.1.) Modelling using second order differential equations a) Find the ODE that models of the motion...
.1.) Modelling using second order differential equations a) Find the ODE that models of the motion of the dumped spring mass system with mass m=1, damping coefficient c=3, and spring constant k=25/4 under the influence of an external force F(t) = cos (2t). b) Find the solution of the initial value problem with x(0)=6, x'(0)=0. c) Sketch the graph of the long term displacement of the mass m.
Consider the differential equation y′′+ 9y′= 0.( a) Let u=y′=dy/dt. Rewrite the differential equation as a...
Consider the differential equation y′′+ 9y′= 0.( a) Let u=y′=dy/dt. Rewrite the differential equation as a first-order differential equation in terms of the variables u. Solve the first-order differential equation for u (using either separation of variables or an integrating factor) and integrate u to find y. (b) Write out the auxiliary equation for the differential equation and use the methods of Section 4.2/4.3 to find the general solution. (c) Find the solution to the initial value problem y′′+ 9y′=...
A 128 lb weight is attached to a spring whereupon the spring is stretched 2 ft...
A 128 lb weight is attached to a spring whereupon the spring is stretched 2 ft and allowed to come to rest. The weight is set into motion from rest by displacing the spring 6 in above its equilibrium position and also by applying an external force F(t) = 8 sin 4t. Find the subsequent motion of the weight if the surrounding medium offers a negligible resistance.
Logistic Equation The logistic differential equation y′=y(1−y) appears often in problems such as population modeling. (a)...
Logistic Equation The logistic differential equation y′=y(1−y) appears often in problems such as population modeling. (a) Graph the slope field of the differential equation between y= 0 and y= 1. Does the slope depend on t? (b) Suppose f is a solution to the initial value problem with f(0) = 1/2. Using the slope field, what can we say about fast→∞? What can we say about fast→−∞? (c) Verify that f(t) =11 +e−tis a solution to the initial value problem...
A 6lb wieght can stretch a spring 6 inches. Suppose the weight is pulled 4 inches...
A 6lb wieght can stretch a spring 6 inches. Suppose the weight is pulled 4 inches past the equilibrium point and released from rest. The initial equation is y(t)=1/3*cos(8t)+0*sin(8t) Suppose that a damping force given in pounds numerically by 1.5 times the instantaneous velocity in feet per second acts on the 6lb weight. Find the position x of the weight as a funtion of time.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT