A 96 lb weight stretches a spring 3.2 ft in equilibrium. It is attached to a dashpot with damping constant c = 18 lb-sec/ft. The weight is initially displaced 15 inches below equilibrium and given a downward velocity of 12 ft/sec. Find its displacement (in feet) for t > 0.
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- A 0.15 kg block oscillates back and forth along a straight line on a frictionless horizontal surface. Its displacement from the origin is given by x=(16 cm)cos[(15 rad/s)t + /2 rad] (a) What is the oscillation frequency? (b) What is the maximum speed acquired by the block? (c) At what value of x does this occur? (d) What is the magnitude of the maximum acceleration of the block? (e) At what positive value of x does this occur? (f) What force, applied to the block by the spring, results in the given oscillation? (a) Number Units (b) Number i Units (c) Number i Units (d) Number i Units (e) Number i Units (f) Number i UnitsA mass of 2 kg on a spring with k = 6 N/m and a damping constant c= 4 Ns/m. Suppose Fo = v2 N. Using forcing function Fo cos(wt), find the w that causes practical resonance and find the amplitude.In the figure, block 2 of mass 2.60 kg oscillates on the end of a spring in SHM with a period of 18.00 ms. The position of the block is given by x = (1.70 cm) cos(wt + T/2). Block 1 of mass 5.20 kg slides toward block 2 with a velocity of magnitude 7.50 m/s, directed along the spring's length. The two blocks undergo a completely inelastic collision at time t = 4.50 ms. (The duration of the collision is much less than the period of motion.) What is the amplitude of the SHM after the collision? 2010 Number Units m 2.
- 1 4. The plot below shows the velocity of a hockey puck as a function of time. The puck starts at time t=0 at position x-3 m in the positive direction. All quantities are measured in SI units (meters and seconds). v (m/s) -1 1 2 4 t(s) a) Draw sketches of corresponding position versus time and acceleration versus time for the puck. The time axis is identical for all 3 graphs/sketches (this one, position, acceleration graphs) At time t-4s, what is the puck's position? At time t-3s, what is the puck's acceleration?A thrill-seeking cat with mass 4.00 kg is attached by a harness to an ideal spring of negligible mass and oscillates vertically in SHM. The amplitude is 0.050 m, and at the highest point of the motion the spring has its natural unstretched length. Calculate the elastic potential energy of the spring (take it to be zero for the unstretched spring), the kinetic energy of the cat, the gravitational potential energy of the system relative to the lowest point of the motion, and the sum of these three energies when the cat is (b) at its lowest point found the answer on quizlet but i cannot understand the Us part. it says Us= mgh yet there is a times 2 before 0.05 (check picture for context) please explain it to me. thanksA spring oscillator is designed with a mass of 0.288 kg. It operates while immersed in a damping fluid, selected so that the oscillation amplitude decreases to 1.00% of its initial value in 7.55 s. Determine the damping coefficient b of the system. Assume that the system is underdamped. b = kg/s
- A particle undergoes simple harmonic motion with angular velocity of 3.0 rad/s and amplitude of 0.5 m. It starts with maximum forward displacement at time t = 0. Find the velocity at time t = 2.0 sA 2-kg mass is attached to a spring with stiffness 56 N/m. The damping constant for the system is 8√√7 N-sec/m. If the mass is pulled 10 cm to the right of equilibrium and given an initial rightward velocity of 4 m/sec, what is the maximum displacement from equilibrium that it will attain?A 3-kg mass is attached to a spring with stiffness 60 N/m. The damping constant for the system is 12√5 N-sec/m. If the mass is pulled 20 cm to the right of equilibrium and given an initial rightward velocity of 4 m/sec, what is the maximum displacement from equilibrium that it will attain?
- A block is attached to a spring with a sping constant of 7.6 N/m and it undergoes simple harmonic motion. The amplitude of the blocks motion is 6.30 cm. When the block is halfway between its equilibrium position and the end point of it's motion, its speed is measured to be 28.9 cm/s. Calculate : (a) the mass of the block, (b) the period of the motion, and (c) the maximum acceleration of the block.A 60.0-g object connected to a spring with a force constant of 40.0 N/m oscillates with an amplitude of 5.00 cm on a frictionless, horizontal surface. (a) Find the total energy of the system.(b) Find the speed of the object when its position is 1.30 cm. (Let 0 cm be the position of equilibrium.)(c) Find the kinetic energy when its position is 3.50 cm.(d) Find the potential energy when its position is 3.50 cm.Two massless springs with spring constants 610 N/m and 116 N/m are hung from a hor- izontal support. A block of mass 6 kg is suspended from the pair of springs, as shown. When the block is in equilibrium, each spring is stretched an additional Ar. Then the block oscillates with an amplitude of 49 m and it passes through its equilibrium point with a speed of 539 m/s. 610 N/m -oooo² 6 kg -0000² 116 N/m What is the angular velocity of this system? The acceleration due to gravity is 9.8 m/s. 1. w = 15 2. w = 2 3. w = 11 rad/s 4. w = 13 5. w = 21 6. w = 16 7. w = 8 X 8. w = 4 9. w = 6 10. = 18