Example 5.5 A particle executes S.H.M. of period 10 sec. and amplitude 5 cm. Calculate the maximum amplitude of velocity.

Consider a particle moving in uniform circular motion in the xy plane at a distance r = 1.1 m from the origin. Refer to the figure. In this problem, you will show that the projection of the particle’s motion onto the x-­axis can be used to represent simple harmonic motion. a. If the particle moves counterclockwise at a constant angular velocity of ω, and at time t = 0 its coordinates are (x,y) = (r,0), enter an expression for the projection of the particle’s position onto the x-axis, in terms of r, ω, and t.  b.  For an angular speed of ω = 7.4 rad/s, find the value of x, in meters, at time t = 0.44 s.  c.  Considering the expression you entered in part (a) for the projection of the particle’s position onto the x-axis, can the projection’s motion be described as simple harmonic motion?   d. Which of the graphs correctly shows the projection of the position of the moving particle onto the x-axis as a function of t for two full cycles?   e.  Enter an expression for the velocity function,…

A fan is spinning trying to cool down people during a hot summers day. It has a period of 0.940 s and a diameter of 26.8 cm. It begins to slow down and it stops after 5.00 s. How many revolutions did the fan make between the time it started to slow down and when it stopped? a) 2.66 revb) 7.98 revc) 16.7 revd) 137 rev