Question

Consider the spring-mass system whose motion is governed by the initial value problem d^2y/dt 2 +...

Consider the spring-mass system whose motion is governed by the initial value problem d^2y/dt 2 + 16y = 0, y(0) = 24, y ′ (0) = −28.

Determine the circular frequency of the system and the amplitude

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
We consider a spring mass system. We use standard international system of units, the mass is...
We consider a spring mass system. We use standard international system of units, the mass is 1kg and the change of magnitude of force |∆Fs| (in unit of Newton, 1N = 1kg ∗ m/s2) from the spring is 9 times the change of length of the spring |∆x|(in meter), i.e |∆Fs| = |9∆x|, the spring is a linear spring with spring constant equal to 3 in Hook’s law. The equilibrium position is at x = 0. When the external forcing...
2. Consider a spring-mass-damper system with the equation of motion given by: ?̈+ 2?̇ + 122?...
2. Consider a spring-mass-damper system with the equation of motion given by: ?̈+ 2?̇ + 122? = 0 a) Is the system overdamped, underdamped or critically damped? Does the system oscillate? If the system oscillates, compute the frequency of the oscillations in rad/s and Hz. b) Determine the displacement response if the initial conditions are ?0 = −1 mm and ?0 = 12 mm/s
Solve the initial value problem. 5d^2y/dt^2 + 5dy/dt - y = 0; y(0)=0, y'(0)=1
Solve the initial value problem. 5d^2y/dt^2 + 5dy/dt - y = 0; y(0)=0, y'(0)=1
3. Consider a spring-mass-damper system with the equation of motion given by: ?̈+ 7?̇ + 10?...
3. Consider a spring-mass-damper system with the equation of motion given by: ?̈+ 7?̇ + 10? = 0 c) Is the system overdamped, underdamped or critically damped? Does the system oscillate? If the system oscillates, compute the frequency of the oscillations in rad/s and Hz. d) Determine the displacement response if the initial conditions are ?0 = 2 mm and ?0 = −7 mm/s
Consider the initial value problem my′′+cy′+ky=F(t), y(0)=0, y′(0)=0 modeling the motion of a spring-mass-dashpot system initially...
Consider the initial value problem my′′+cy′+ky=F(t), y(0)=0, y′(0)=0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m=2 kilograms, c=8 kilograms per second, k=80 Newtons per meter, and F(t)=60cos(8t) Newtons. Solve the initial value problem. y(t)= help (formulas) Determine the long-term behavior of the system. Is limt→∞y(t)=0? If it is, enter zero. If not, enter a function that approximates y(t) for...
1. Solve the following initial value problem using Laplace transforms. d^2y/dt^2+ y = g(t) with y(0)=0...
1. Solve the following initial value problem using Laplace transforms. d^2y/dt^2+ y = g(t) with y(0)=0 and dy/dt(0) = 1 where g(t) = t/2 for 0<t<6 and g(t) = 3 for t>6
Initial value problem : Differential equations: dx/dt = x + 2y dy/dt = 2x + y...
Initial value problem : Differential equations: dx/dt = x + 2y dy/dt = 2x + y Initial conditions: x(0) = 0 y(0) = 2 a) Find the solution to this initial value problem (yes, I know, the text says that the solutions are x(t)= e^3t - e^-t and y(x) = e^3t + e^-t and but I want you to derive these solutions yourself using one of the methods we studied in chapter 4) Work this part out on paper to...
solve the given initial value problem dx/dt=7x+y x(0)=1 dt/dt=-6x+2y y(0)=0 the solution is x(t)= and y(t)=
solve the given initial value problem dx/dt=7x+y x(0)=1 dt/dt=-6x+2y y(0)=0 the solution is x(t)= and y(t)=
Consider the initial value problem mx′′+cx′+kx=F(t),   x(0)=0,   x′(0)=0 modeling the motion of a damped mass-spring system initially at...
Consider the initial value problem mx′′+cx′+kx=F(t),   x(0)=0,   x′(0)=0 modeling the motion of a damped mass-spring system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m=2 kilograms, c=8 kilograms per second, k=80 Newtons per meter, and F(t)=30e−t Newtons. Solve the initial value problem. x(t)= Determine the long-term behavior of the system (steady periodic solution). Is limt→∞x(t)=0? If it is, enter zero. If not, enter a function that approximates x(t) for...
Consider the forced spring-mass system: d^2x/dt^2 + ω^2 x = A sin (ωt) (3) where in...
Consider the forced spring-mass system: d^2x/dt^2 + ω^2 x = A sin (ωt) (3) where in general ω ̸= ω0. (a) Find the general solution to equation (3). (b) Find the solution appropriate for the initial conditions x(0) = 0 and dx dt (0) = 0. (c) Let’s explore what happens as resonance is approached: Let ω = ω0 (1 + ϵ), where ϵ ≪ 1. Expand your solution in (b) using the idea of a Taylor series about ω0...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT