Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

A 0.84 kg block is attached to a spring andallowed to oscillate. The displacemen

ID: 1679035 • Letter: A

Question

   A 0.84 kg block is attached to a spring andallowed to oscillate. The displacement from equilibrium as afunction of time is given by: x = (10 cm) cos (2 rad/s t + ) a) Find the maximum kinetic energy. b)Find the maximum force exerted by the spring. c)Find the displacement when the velocity is ¼ of itsmaximum.    A 0.84 kg block is attached to a spring andallowed to oscillate. The displacement from equilibrium as afunction of time is given by: x = (10 cm) cos (2 rad/s t + ) a) Find the maximum kinetic energy. b)Find the maximum force exerted by the spring. c)Find the displacement when the velocity is ¼ of itsmaximum. c)Find the displacement when the velocity is ¼ of itsmaximum.

Explanation / Answer

Mass m = 0.84 kg

The displacement from equilibrium as a function of time isx = (10 cm) cos (2 rad/s t + )

Compare this with x = A cos ( wt + )

We get amplitude A= 10 cm =0.1 m

Angular frequency w= 2 rad / s

a) the maximum kinetic energy K = ( 1/ 2) mw^ 2 A ^ 2

                                                     = 0.0168 J

b)the maximum force exerted by the spring F max = KA

                                                                                = mw^ 2 * A

                                                                                  = 0.336 N

velocity v = V max / 4