10. A mass-spring system moves with simple harmonic motion along the x axis between turning points at x, = 20 cm and x= 60 cm. For parts (i) through (iii), choose from the same five possibilities. (i) At which position does the particle have the greatest magnitude of momentum? (a) 20 cm (b) 30 cm (c) 40 cm (d) some other position (e) The greatest value occurs at multiple points. (ii) At which position does the particle have greatest kinetic energy? (iii) At which position does the particle-spring system have the greatest total energy?

A block of mass M = 8 kg rests on a horizontal frictionless floor, and is connected to a vertical wall by a spring of force constant k = 200 N/m. When the spring is in its equilibrium position (neither stretched nor compressed), the block just touches a second lighter block of mass m = 4 kg at rest on the frictionless floor. The spring with mass M attached is now compressed by 0.1 m and released. The two blocks undergo a completely inelastic collision, i.e., they stick together after collision. Draw a diagram and define all relevant variables. Just before the collision, what is the velocity of mass MT Just after the collision, what is the common velocity of the two blocks? (What is the maximum stretching of the spring after the collision?: How long after the collision do the masses reach their first maximum stretch?

2. (30%) Given an undamped linear vibration system, a ramp input of the form F(t)=Fot is applied. (1) For the case of m=2 Kg, k=200 N/m and Fo=100 N/s, formulate the impulse response function h(t); (2) Find the time response x(t) of the system 2ä(t) + 200x(t) = 100t

A 0.2-kg pendulum bob A hangs from a 0.75 m cord attached to a fixed pivot. It is released from rest at point 1 when the cord is horizontal and without slack, and swings down to strike 0.2-kg bob B at point 2. The coefficient of restitution between the two bobs is e = 0.7. Neglect the size of the bobs and the mass of the cords. 0.75 m 1 For parts b-f below, consider bob A at the instant the cord is vertical, when it has reached point 2, and immediately before the collision: a) ) What is the tension in the cord of the stationary bob B? b) ( Draw a clear and complete free body diagram of bob A. с) ( Find the speed of bob A. d) Find the tangential acceleration of bob A. e) Find the normal acceleration of bob A. f) Find the tension in the cord of bob A. g) Find the speed of bob A immediately after the collision.