A spring with a mass of 2 kg has a damping constant 14 kg/s. A force of 3.6 N is required to keep the spring stretched 0.3 m beyond its natural length. The spring is stretched 0.6 m beyond its natural length and then released. Find the position of the mass at any time t. (Assume that movement to the right is the positive x-direction and the spring is attached to a wall at the left end.)
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- A mass of 1.79 kg is placed on a vertical spring. What is the spring constant, in N/m, of a mass-spring system with a period of 0.7 s?A simple pendulum is suspended from the ceiling by means of a string and has a length of 1.56 m long. Suppose you start with the pendulum hanging vertically, at rest. You then give it a push so that it starts swinging with a speed of 1.73 m/s. What maximum angle (in degrees) will it reach, with respect to the vertical, before falling back down? 38.3 degrees 31.9 degrees 25.5 degrees 20.4 degreesA 0.282 kg mass is attached to a spring with a spring constant 197 N/m so that the mass is allowed to move on a horizontal frictionless surface. The mass is released from rest when the spring is compressed 0.145 m. Find the maximum force on the mass. Answer in units of N.
- A spring with a spring constant of k = 192 N/m is initially compressed by a block a distance d = 0.23 m. The block is on a horizontal surface with coefficient of kinetic friction μk, static friction μs, and has a mass of m = 7 kg. How large would the coefficient of static friction μs need to be to keep the block from moving? Recall that to keep the block from moving, the acceleration is zero. Assuming the block has just begun to move and the coefficient of kinetic friction is μk = 0.2, what is the block's acceleration in meters per square second?This time the pendulum is 2.42 m long. Suppose you start with the pendulum hanging vertically, at rest. You then give it a push so that it starts swinging with a speed of 2.68 m/s. What maximum angle (in degrees) will it reach, with respect to the vertical, before falling back down? 41.5 degrees 36.7 degrees 31.9 degrees 16.0 degreesA spring-mass system has a spring with spring constant k=85.0 N/m and a 650.0 gram mass on the end of the spring. The surface supporting the mass is frictionless and there is negligible air resistance. When the system is first observed (at time t = 0), the spring is stretched 13.20 cm from its natural length and the velocity of the mass is 1.90 m/s in the +x direction. 1. What is the displacement function x(t) for this motion? 2. If the spring-mass system was placed in a chamber where the air resistance has a drag constant of b = 1.40, what is the frequency of the new system, in rad/s? Round to the nearest hundredth (0.01). Justify your answer using your rationale and equations used.
- You hang different masses M from the lower end of a vertical spring and measure the period T for each value of M. You use Excel to plot T2 (in s2) on the y-axis versus M (in kg) on the x-axis. The equation for the straight line that gives the best fit to your data is y = 0.0467x + 0.00400. (a) What is the mass of the spring? I found that the force constant of the spring is 845.362 N/m and for the mass of the spring I found it to be 0.085 kg (85.65 g) but it's wrong when I submit it. Am I doing something wrong?A mass of 6.33 kg is placed on a vertical spring. What is the spring constant, in N/m, of a mass-spring system with a period of 0.6 s?This time the pendulum is 1.37 m long. Suppose you start with the pendulum hanging vertically, at rest. You then give it a push so that it starts swinging with a speed of 1.12 m/s. What maximum angle (in degrees) will it reach, with respect to the vertical, before falling back down? 7.0 degrees 29.9 degrees 23.8 degrees 17.6 degrees
- A patio swing is suspended by two springs, each of which has a force constant of 430 N/m, equivalent to a single spring force constant of 860 N/m. Find the mass of a person sitting on the swing oscillating up and down at a frequency of 0.515 Hz.As shown below, a 3 kg block on a frictionless horizontal surface is attached to a cable and a 526 N/m spring. The block is in equilibrium (Fnet = 0) and the cable has a tension of 16 N. Determine the normal force on the block and how much the spring stretched. FN l=| xA mass of 0.50 kg is held against compressed spring and released from rest while upon a horizontal, frictionless surface. The spring constant of the spring is 790 N/m and the mass leaves the spring with a speed of 7.84 m/s. Assume that the spring pushes the mass across the surface. By what amount was the spring initially compressed relative to its equilibrium position? 0.197