Show that (1/2)mv^2 and (1/2)kx^2 carry the same units, assuming m is mass, v is velocity, k is the spring constant, and x is position.
Show that (1/2)mv^2 and (1/2)kx^2 carry the same units, assuming m is mass, v is velocity,...
Please show all work
A ball of mass M with an initial velocity vo=0 m/s is shot at an angle o upward by the release of a spring of constant k that is compressed a distance x. The ball falls back to the ground. Assuming that the ball falls back to its original height, what is the final velocity of the ball? O Wikx2/M)cose-V(kx2/M) OV(kx2/M) OV(kx2/M)-((kx?/M)sine OW(kx?/M)sine-v(kx2/M) OV(kx2/M)-((kx2/M)cose
A linear spring-mass system (without friction) satisfies m(d^2x/dt^2) = -kx, Derive that m/2 (dx/dt)^2 + k/2 x^2 = constant = E. Consider the initial value problem such that at t = 0, = x_0 and dx/dt = v_0. Evaluate E. Using the expression for conservation of energy, evaluate the maximum displacement of the mass from its equilibrium position. Compare this to the result obtained from the exact explicit solution.
1) A railroad car of mass 2,000 kg traveling at a velocity v = 10 m/s is stopped at the end of the tracks by a spring-damper system, as shown below. If the stiffness of the spring is k= 40 N/mm and the damping constant c 20 N-s/mm, determine (a) the maximum displacement of the car after engaging the springs and damper, (b) the time taken to reach maximum displacement k2 P 0000 k/2
1) A railroad car of mass...
9. A mass m is attached to a massless spring with a force constant k. The mass rests on a horizontal, frictionless surface. The system is compressed a distance x from the spring's initial position and then released. The momentum of the mass when the spring passes its equilibrium position is given by (A) xvmek (B) x/k/m o x/m/k (D) x/km + KxP = {mv² p=mv
11. An Object moving with uniform acceleration has a velocity of 1.2 m/s when x=3cm. What is the objects acceleration if 3 seconds later the object's position is x=-12cm? 2. If the Energy of a mass on a vibrating spring is represented by E= k V t, where "V" is the volume of the mass on the spring, and "t" is for time. What units must the constant “k" have in order for the equation to be dimensionally correct.
Question 2 A simple harmonic oscillator is made up of a mass-spring system, with mass of 2.39 kg and a spring constant k = 140 N/m. At time t=1.66 s, the position and velocity of the block are x = 0.113 m and v = 3.692 m/s. What is the velocity of the oscillation at t=0? Be sure to include the minus sign for negative velocity. Your answer should be in m/s, but enter only the numerical part in the...
Please Show steps
(1 point) This problem is an example of over-damped harmonic motion. A mass m = 3 kg is attached to both a spring with spring constant k = 36 N/m and a dash-pot with damping constant c= 24 N · s/m. The ball is started in motion with initial position xo = -4 m and initial velocity vo = 2 m/s. Determine the position function x(t) in meters. X(t) = Graph the function x(t).
A mass weighing 8 pounds lengthens a spring by 2 feet
assuming that a damped force equal to 2 times the instantaneous
velocity and acting
on the system determines the equation of motion if the initial mass
is released from the equilibrium position with a velocity ascending
3 ft / s. Solve the previous exercise with La Place transforms
m d2x dx + B + kx = 0 dt dt m = 0.25 pulg k = 4 lb/ft B =...
Please report your answer to 2 significant figures. As shown below, a block of mass m = 0.37 kg is initially at rest on a frictionless inclined plane at height = 5m and pressed against a spring so that the spring is compressed by an amount x = 2.7 m. Using conservation of mechanical energy, please find the speed of the block after it has lost contact with the spring and has reached a height he = 14 m. The...
2. Following problem 1, the same spring-mass is oscillating, but the friction is involved. The spring-mass starts oscillating at the top so that its displacement function is x Ae-yt cos(wt)t is observed that after 5 oscillation, the amplitude of oscillations has dropped to three-quarter (three-fourth) of its initial value. (a) 2 pts] Estimate the value ofy. Also, how long does it take the amplitude to drop to one-quarter of initial value? 0 Co [2 pts] Estimate the value of damping...