1. An object with mass 5 kg is attached to a spring with spring constant 20 kg/sec². The spring is pulled down 0.5 m, and is released with an initial upward velocity of 3 m/s. Find the position of the spring at time t.
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- 2. Construct a problem where a mass is sitting on top of a spring inside an elevator; both are suspended by a rope and are uniformly accelerating upwards with magnitude 4 meters per second squared. Specify all the masses in the problem, as well as all the forces acting in the problem, and their relative directions.A 2.0 kg object compresses a spring with a spring constant of 100 N/m by a distance of 8 cm, and then the object is released. Assuming that the object maintains the same acceleration while the spring returns to equilibrium, how fast is the object moving after 1.2 s?The y-coordinate of a particle varies at a constant speed of 4.2 m/s. At t=0, the y-coordinate was found to be 2.7 m. Find an analytic expression for the function y(t).
- A student hangs different masses on a vertical spring and measures its length each time. Trial Mass (g) Length (cm) 1 50 25.6 2 100 31.2 3 150 36.8 Find the spring constant in units of N/m-1Find the instantaneous velocity of the particle described in the figure below at the following times. x(m) 10 8 6 4 2 0 -2 -4 (a) t = 1.5 s 1 (b) t = 3.4 s (c) t = 4.6 s (d) t = 7.3 s 2 3 m/s m/s m/s m/s 4 5 6 7 8 -l(s)4. A simple pendulum is suspended from the ceiling by means of a string of length 1.44 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 1.53 m/s. What maximum angle (in degrees) will it reach, with respect to the vertical, before falling back down? 32.9 degrees 28.2 degrees 23.5 degrees 16.5 degrees