A puck of mass, m, is attached to an elastic cord of unstretched length, L. The cord obeys Hooke's law and has a spring constant, k. The puck rests on a horizontal frictionless table and is swung around with constant angular velocity, w. Find an expression for the displacement of the elastic cord in terms of k, m, w, and L.

A 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.

A car with mass 1530 kg crashes into a wall. The car’s velocity immediately before the collision was 12.6 m/s and the bumper is compressed like a spring with spring constant 1.14 × 107 N/m. What is the maximum deformation of the bumper for this collision?Answer in units of m.

A cube, whose mass is 0.700 kg, is attached to a spring with a force constant of 110 N/m. The cube rests upon a frictionless, horizontal surface (shown in the figure below). A cube labeled m is attached to the right end of a horizontal spring, and the left end of the spring is attached to a wall. The spring is stretched horizontally such that the cube is displaced by a distance A to the right of its equilibrium position. The cube is pulled to the right a distance A = 0.110 m from its equilibrium position (the vertical dashed line) and held motionless. The cube is then released from rest. (a) At the instant of release, what is the magnitude of the spring force (in N) acting upon the cube?  N (b) At that very instant, what is the magnitude of the cube's acceleration (in m/s2)?  m/s2 (c) In what direction does the acceleration vector point at the instant of release?