Question

. A mass is attached to a spring. The position of the mass as it oscillates on the spring is given by: y = A cos (8.2t) where the value of t is in seconds and A is 6.2 cm. (a) What is the period of the oscillator? (2 pts)





(b) What is the velocity of the oscillator at time t = 0 and at time t = T/4? Give magnitude and direction (+ or – y direction). (4 pts)






(c) If the attached mass is 1.2 kg, find the value of the force constant for the spring (k). (3 pts)







(d) What is the acceleration of the oscillator at t = 0? Give both magnitude and direction. (4 pts)







(e) What is the kinetic energy of the oscillator at y = A/3? What fraction of total energy is the kinetic energy at this point? (4 pts)







(f) If you were asked to double the period of the oscillator by using a different mass (with the same spring), would you need a larger mass or a smaller mass? What is this new mass? (3 pts)

Answer 1

with A Cos t Campaing w 8.2edrc Sec T- 2 0.76 8.2 (b) A Cos (8-2)t = daAx8-2 sin (6-2 t) dt At to. no) 6.2x 8-2 Cmsec = omlsrc 1 M/sec At tnly (c) K=mw-2-2)^ 8.69 N/ -Ay 8.y 82 Cos (8-t dt at to AX 8-2y &2 n/se02 6-2xf- & Com/sec Totd Enery 4KA