Question

Determine C1 and C2 of the following damped motion A 4-lb weight stretches a spring 4...

Determine C1 and C2 of the following damped motion

A 4-lb weight stretches a spring 4 ft. Initially the weight released from 2ft above equilibrium position with downward velocity 2 ft/sec. Find the equation of motion x(t), provided that the subsequent motion takes place in a medium that offers a damping force numerically equal to (1/2) times the instantaneous velocity

Homework Answers

Answer #1

ANSWER:-----

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
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...
A mass weighing 19.6 N stretches a spring 9.8 cm. The mass is initially released from...
A mass weighing 19.6 N stretches a spring 9.8 cm. The mass is initially released from a point 2/3 meter above the equilibrium position with a downward velocity of 5 m/sec. (a) Find the equation of motion. (b)Assume that the entire spring-mass system is submerged in a liquid that imparts a damping force numerically equal to β (β > 0) times the instantaneous velocity. Determine the value of β so that the subsequent motion is overdamped.
A mass weighing 4 pounds is attached to a spring whose constant is 2 lb/ft. The...
A mass weighing 4 pounds is attached to a spring whose constant is 2 lb/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 12 ft/s. Determine the time at which the mass passes through the equilibrium position. (Use g = 32 ft/s2 for the acceleration due to gravity.) s Find the time after the mass...
DIFFERENTIAL EQUATIONS 1. A force of 400 newtons stretches a spring 2 meters. A mass of...
DIFFERENTIAL EQUATIONS 1. A force of 400 newtons stretches a spring 2 meters. A mass of 50 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 10 m/s. Find the equation of motion. 2. A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to times the...
A mass weighing 24 pounds attached to the end of the spring and stretches it 4...
A mass weighing 24 pounds attached to the end of the spring and stretches it 4 inches. The mass is initially released from rest from a point 3 inches above the equilibrium position with a downward velocity of 2 ft/sec. Find the equation of the motion?  
A mass weighing 3 lb stretches a spring 3 in. If the mass is pushed upward,...
A mass weighing 3 lb stretches a spring 3 in. If the mass is pushed upward, contracting the spring a distance of 1 in, and then set in motion with a downward velocity of 2 ft/s, and if there is no damping, find the position u of the mass at any time t. Determine the frequency, period, amplitude, and phase of the motion
A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to...
A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to 2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 9 ft/s. (Use g = 32 ft/s2 for the acceleration due to gravity.) x(t) = Find the time at which the mass attains its...
A force of 400N stretches a string 2 meters. A mass of 50kg is attached to...
A force of 400N stretches a string 2 meters. A mass of 50kg is attached to the end of the spring and stretches the spring to a length of 4 meters. The medium the spring passes through creates a damping force numerically equal to half the instantaneous velocity. If the spring is initially released from equilibrium with upward velocity of 10 m/s. a) Find the equation of motion. b) Find the time at which the mass attains its extreme displacement...