A 0.00140 kg bullet strikes a 0.257 kg block attached to a fixed horizontal spring whose spring constant is 2250 N/m and sets it into oscillation with an amplitude of 12.4 cm. What was the initial speed of the bullet if the two objects move together after impact?

The device pictured in the figure entertains infants while keeping them from wandering. The child bounces in a harness, with a spring constant k, and is suspended off of the ground. Part (a)  If the spring stretches x1 = 0.26 m from equilibrium while supporting an 7.45-kg child, what is its spring constant, in newtons per meter?  Part (b)  What is the time, in seconds, for one complete bounce of this child about the point x1?  Part (c)  What is the child’s maximum velocity, in meters per second, if the amplitude of her bounce, relative to x1, is 0.175 m?

A mass of 0.43 kg is is initially traveling at across a horizontal surface. It then reaches a spring with a fixed end having a spring constant of 138 N/m that is positioned horizontally and initially at equilibrium. If the initial speed of the mass is 3.81 as it contacts the spring, what is the speed of the mass after compressing the by 0.153 m if the coefficient of kinetic friction is between the surfaces is 0.47 ?

Astronauts in space cannot weigh themselves by standing on a bathroom scale. Instead, they determine their mass by oscillating on a large spring. Suppose an astronaut attaches one end of a large spring to her belt and the other end to a hook on the wall of the space capsule. A fellow astronaut then pulls her away from the wall and releases her. The spring's length as a function of time is shown in the figure (Figure 1). Figure L (m) 1.4 1.2 1.0 0.8 0.6 0.4- 0.2 0.0 0 3 < v 6 1 of 1 -t (s)