Question

A spring-mass system has a spring constant of 3 Nm. A mass of 2 kg is...

A spring-mass system has a spring constant of 3 Nm. A mass of 2 kg is attached to the spring, and the motion takes place in a viscous fluid that offers a resistance numerically equal to the magnitude of the instantaneous velocity. If the system is driven by an external force of 15cos(3t)−10sin(3t) N,determine the steady-state response in the form Rcos(ωt−δ).

R=    

ω=    

δ=

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is...
A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is attached to the spring, and the motion takes place in a viscous fluid that offers a resistance numerically equal to the magnitude of the instantaneous velocity. (a) If the system is driven by an external force of (12 cos 3t − 8 sin 3t) N, determine the steady-state response. (b) Find the gain function if the external force is f(t) = cos(ωt). (c) Verify...
A mass of 4 Kg attached to a spring whose constant is 20 N / m...
A mass of 4 Kg attached to a spring whose constant is 20 N / m is in equilibrium position. From t = 0 an external force, f (t) = et sin t, is applied to the system. Find the equation of motion if the mass moves in a medium that offers a resistance numerically equal to 8 times the instantaneous velocity. Draw the graph of the equation of movement in the interval.
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released from rest from a point 3 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1 2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 20 cos(3t). (Use g = 32 ft/s2 for the acceleration...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released from rest from a point 3 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1 2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 10 cos(3t). (Use g = 32 ft/s2 for the acceleration...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from rest from a point 3 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 10 cos(3t). (Use g = 32 ft/s^2 for the acceleration due to...
3. A mass of 5 kg stretches a spring 10 cm. The mass is acted on...
3. 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. Then (a) Find the...
A particular spring has a spring constant of 50 Newton/meters. Suppose a 1/2 kg mass is...
A particular spring has a spring constant of 50 Newton/meters. Suppose a 1/2 kg mass is hung on the spring and is initially sent in motion with an upward velocity of 10 meters per second, 1/2 meter below the equilibrium position. A) Write down the DE that models the motion of this spring. B) Write down the initial conditions. C) Find the equation of motion for the spring. D) Suppose this spring mass system experiences a viscous damping term that...
A mass of 1 slug, when attached to a spring, stretches it 2 feet and then...
A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at t = 0, an external force equal to f(t) = 4 sin(4t) is applied to the system. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity. (Use g = 32 ft/s2 for the acceleration due to gravity.) What is x(t) ?...
Solve the following differential equations. A spring has a constant of 4 N/m. The spring is...
Solve the following differential equations. A spring has a constant of 4 N/m. The spring is hooked a mass of 2 kg. Movement takes place in a viscous medium that opposes resistance equivalent to instantaneous speed. If the system is subjected to an external force of (4 cos(2t) - 2 sin(2t)) N. Determine: a. The position function relative to time in the transient state or homogeneous solution b. Position function relative to time in steady state or particular solution c....
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...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT