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

A car tire is 62.0 cm in diameter. The car is traveling at a speed of 16.0 m/s. What is the tire's rotation frequency, in rpmrpm? What is the speed of a point at the top edge of the tire? What is the speed of a point at the bottom edge of the tire?

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The maximum height of a ferris wheel is 11m. The wheel takes 3 min to make 1 turn.People get on the ferris wheel 1m above the ground at the bottom of the wheel’s rotation. a) State the amplitude, period, and vertical shift of the graph. b)Write an equation to represent the model you determined in part a). c) Determine how high the passenger will be at 60 seconds

Context The needle of a sewing machine makes a repetitive up and down motion which is described by the equation                                                                                    y(t)=Acos(wt) To choose the settings of the device that will ensure that the needle successfully pierces the textile, you are asked to model the speed in y of the needle as a function of time. Constraints and information The parameter A represents the range of motion (in m);The parameter w represents the angular frequency. It tells us about the number of back and forth movements that the needle makes per second;The parameter w is given in rad/s, so your calculator absolutely must be in radians mode to do the calculations in this problem;This type of movement is called Simple Harmonic Movement and will be studied in depth in the 3rd physics course Modelization Establish the model for the y velocity of the needle as a function of time and the parameters A and w. Then test your model by…

A116 Define sinple harnonic motion, and explain what is meant by the amplitude and period of such a motion.

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,…

Ż str-g with fixed x= A tightly stretched str-g end pants x=0 ad α= L & Intrally is in a position guver by y = y sin 32. 16 it is released for rest from its initial position, find the displacement y (x.t). з пос L

B = (2i + 4)+ 8k) Q2/ A body on a spring oscillates with a period of 2 sec and amplitude of 15 cm .At time equal to zero second ,it is 7 cm to the left of equilibrium and moving to the left .what are its position and direction of motion at time equal to four second? Q3/ A rest particle was accelerated by a circular path of radius 7 m, according to cquation a=9t3 6t213t4I find the angular location for the

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