Question

In: Advanced Math

Differential Equations. A 10kg weight is attached to a wall horizontally via a spring. The rest...

Differential Equations. A 10kg weight is attached to a wall horizontally via a spring. The rest (equilibrium) length of the spring is 0.2m. The spring has stiffness coefficient k = 50. The weight drags along the ground, giving an effective damping coefficient of b = 40. We will ignore gravity and all other outside forces on the spring. If the weight is pulled to a position 0.5m away from the wall (thus +0.3m past equilibrium) and then flicked toward the wall at 2m/s. How close is the weight to the wall after 1 second? Bonus question: What is the closest the weight gets to the wall? Must use differential equations formula not physics

Solutions

Expert Solution


Related Solutions

A 10kg weight is attached to a wall horizontally via a spring. The rest (equilibrium) length...
A 10kg weight is attached to a wall horizontally via a spring. The rest (equilibrium) length of the spring is 0.2m. The spring has stiffness coefficient k = 50. The weight drags along the ground, giving an effective damping coefficient of b = 40. We will ignore gravity and all other outside forces on the spring. If the weight is pulled to a position 0.5m away from the wall (thus +0.3m past equilibrium) and then flicked toward the wall at...
DIFFERENTIAL EQUATIONS An 8-lb weight is attached to the lower end of a coil spring suspended...
DIFFERENTIAL EQUATIONS An 8-lb weight is attached to the lower end of a coil spring suspended from a fixed support. The weight comes to rest in its equilibrium position, thereby stretching the spring 6 in. The weight is then pulled down 9 in. below its equilibrium position and released at t=0. The medium offers a resistance in pounds numerically equal to 4x', where x' is the instantaneous velocity in feet per second. Determine the displacement of the weight as a...
DIFFERENTIAL EQUATIONS: 1. A body with a weight of 3.5 grams force hangs from a spring...
DIFFERENTIAL EQUATIONS: 1. A body with a weight of 3.5 grams force hangs from a spring stretching it 3.21 centimeters. Initially the body starts from rest 3.4 centimeters below its equilibrium position. The medium in which the body moves offers a resistance force to movement that is numerically equal to 1/8 of its instantaneous speed. Knowing that there is an external force, changing in time, which is defined by the formula: f (t) = 7cos (t) grams force. Find the...
A 5 kg block is attached to a horizontally-mounted spring with a spring constant of 600...
A 5 kg block is attached to a horizontally-mounted spring with a spring constant of 600 J/m2. The spring is extended by 10 cm from its normal length and the block is then released with an additional pull that imparts an initial velocity of 50 cm/s. The angular velocity (in rad/s) is A rad/s. The phase shift or off set (in degrees) is B degrees. The amplitude (in cm) is C cm. Please highlight where the given mass, spring constant,...
1. A block of mass m attached to a spring with spring constant k oscillates horizontally...
1. A block of mass m attached to a spring with spring constant k oscillates horizontally on a frictionless table. Its velocity is 20 cm/s when x = -5 cm. Taking m = 100 gm, and spring constant = 2.5 N/m, a) Find out the equations of position, velocity, and acceleration of the ball. Find also the total energy of the block when its velocity was 20 cm/s. b) Oscillating particles generate waves. What will be the equation of a...
An 18.4 kg beam is attached to a wall by a hinge and it hangs out horizontally.
1. An 18.4 kg beam is attached to a wall by a hinge and it hangs out horizontally. From the end of the beam, a 27.1 kg metal sculpture is hung. A cable is attached to the wall above the beam and is attached to the beam. The cable makes an angle of 18.9 degrees with the wall. It attaches to the beam 2/7 of the way down from the hinge. What is the tension in the cable?2. A 31...
A 190 g block attached to a spring with spring constant 2.8 N/m oscillates horizontally on...
A 190 g block attached to a spring with spring constant 2.8 N/m oscillates horizontally on a frictionless table. Its velocity is 20 cm/s when x0 = -5.3 cm . a) What is the amplitude of oscillation? b) What is the block's maximum acceleration? c) What is the block's position when the acceleration is maximum? d) What is the speed of the block when x1 = 2.7 cm ?
A 170 g block attached to a spring with spring constant 2.1 N/m oscillates horizontally on...
A 170 g block attached to a spring with spring constant 2.1 N/m oscillates horizontally on a frictionless table. Its velocity is 19 cm/s when x0 = -4.0 cm . A) What is the amplitude of oscillation? B) What is the block's maximum acceleration? C) What is the block's position when the acceleration is maximum? D) What is the speed of the block when x1 = 3.3 cm ?
A 200 g block attached to a spring with spring constant 2.1 N/m oscillates horizontally on...
A 200 g block attached to a spring with spring constant 2.1 N/m oscillates horizontally on a frictionless table. Its velocity is 20 cm/s when x0 = -4.6 cm . A. What is the amplitude of oscillation? B. What is the block's maximum acceleration? C. What is the block's position when the acceleration is maximum? D. What is the speed of the block when x1 = 3.2 cm ?
7) A spring has is stretched horizontally to the right from a wall 0.5 meters by...
7) A spring has is stretched horizontally to the right from a wall 0.5 meters by a force of 40 newtons. This spring has a mass of 10 kg. The mass is pulled to the right (from the equilibrium position) 1 meter and released (at t = 0) with an initial velocity to the right of 2 meters per second. I) Write down the differential equation that governs the motion of the mass. Include the initial conditions. (assume no damping)....
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT