In a hurry to digest this . Tks for the help (thumb up)
In a hurry to digest this . Tks for the help (thumb up) 2. A mass of m kilograms (kg) is mounted on top of a vertical spring. The spring is L metres long when disengaged and the end not attached to t...
A mass of m kilograams (kg) is mounted on top of a vertical spring. The spring is L metres long when disengaged and the end not attached to the mass is fixced to the ground. The mass moves vertically up and down, acted on by gravity, the restoring force T of the spring and the damping force R due to friction: see the diagram below The gravitational force is mg dowswards, where g- 9.8m is acceleration due to gravity, measured...
Just question2(a) please. Thanks 2. An 10 kg object is hung from a spring attached to a fixed support. The spring constant of the spring is k = 40 N m-1. Suppose an external downward force of magnitude f(t) = 20e-2t N is applied to the object, and damping due to air resistance occurs with damping constant B = 40 N s m-1. Let y(t) denote the distance in metres of the object below its equilibrium position at time t...
Suppose a mass of 1 kg is attached to a spring with spring constant k = 2, and rests at equilibrium position. Starting at t = 0, an external force of f(t) = e t is applied to the system. Suppose the surrounding medium offers a damping force numerically equal to β times the instantaneous velocity, where β > 0 is some given number. (a) What is the IVP governing this harmonic motion. (b) For what value(s) of β will...
A 5 kilogram mass suspended from the end of a vertical spring stretches it by 1.225 metres. The system is placed in a medium offering a resistance (in Newtons) equal to 45 times the instantaneous velocity (in m/s). The mass is started in motion from the equilibrium position with an initial velocity of 1 m/s in the upward direction and with an applied external force F(t) 365 cos(3t) Newtons downwards. The displacement of the mass below the equilibrium position at...
A 2kg mass is suspended vertically from a spring attached to a fixed support. The spring satisfies Hooke's law with a spring constant of k 18 N m1. No damping is present. Gravity acts on the mass with a gravitational constant of g 10 m s2. An external force of R 24 sin (wt) Newton is applied to the mass, directed downwards, where t is the time in seconds since the mass was set in motion and w is a...
A mass of 2 kg stretches a spring 0.1 m. At time t= 0 the mass is released from its equilibrium position with a downward velocity of 1 m/s. Air resistance adds a damping force equal to one fifth of the velocity of the mass. Set up an initial value problem for the position x(t) of the mass at time t. Determine whether the system is overdamped, underdamped or critically damped. You can assume the acceleration of gravity g equals...
A spring is suspended vertically from a fixed support. The spring has spring constant k=24 N m −1 k=24 N m−1 . An object of mass m= 1 4 kg m=14 kg is attached to the bottom of the spring. The subject is subject to damping with damping constant β N m −1 s β N m−1 s . Let y(t) y(t) be the displacement in metres at the end of the spring below its equilibrium position, at time t...
Please help with 4a and 4b 4. (8 marks) A spring of natural length L is hung vertically with a mass of 2 kg attached to the end. 4(a) Assume that the friction is negligible and the spring constant is k 128. Find the position of the mass at time t, if the spring is pulled down 0.2m from its equilibrium position and released with velocity 0 at time t = 0. Flo)0.2 4(b) Assume that a spring, with an...
A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position X, and initial velocity vo Find the position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the form x(t) =C, e-pt cos (0,t-a). Also, find the undamped position function u(t) = Cocos (0,0+ - )...
21. A mass weighing 122.5 g stretches a spring by 7- F(f)-0.2e-2 N. The spring is set in motion from its equilibrium position with a downward velocity of I m/s. Find an equation for the position of the spring at any time t. A cm. The damping constant is c 0.4. External vibrations create a force of 32 21. A mass weighing 122.5 g stretches a spring by 7- F(f)-0.2e-2 N. The spring is set in motion from its equilibrium...