Cansomeone explain this problem in quite a bit of detail, step bystep. I have as
ID: 1680845 • Letter: C
Question
Cansomeone explain this problem in quite a bit of detail, step bystep. I have asked this question once before and gotten two answersbut I'm not putting all the pieces together. Thank you.
A uniform rod of mass m and length L is pivoted about an axlethrough one end. The other end is attached to a horizontal masslessspring of spring constant k. The spring is neither stretched norcompressed when the rod hangs straight down. The bottom end of therod is pulled to the right and released. The system oscillates insimple harmonic motion. You can assume the rod’s angle fromthe vertical is always small.
(a)Starting with Newton’s second law for rotation, write adifferential equation for the position of the rod as afunction of time. i.e. write the equation of motion for the system.(Hint: There are two restoring forces acting on therod.)
(b) From the solution to your differential equation,determine the angular frequency
oftherod.(Hint: sincos=1sin(2)) 2
(c)Determine the period of oscillation of the rod.
Explanation / Answer
(a) Starting with Newton’s second law for rotation, writea differential equation for the position of the rod as afunction of time. i.e. write the equation of motion for the system.(Hint: There are two restoring forces acting on therod.)
the two restoring forces on the rod are the spring force andgravitational force
the torque due to these two forces isk*l*lcos+mg*l/2sin=I
where I is the moment of inertia about the axle and isthe angular acceleration=d2/dt2
this completes the differential equation
(b) From the solution to your differential equation,determine the angular frequency
oftherod. (Hint: sincos=1sin(2))2
we have =k*l*lcos+mg*l/2
(c) Determine the period of oscillation of the rod.
pe4riod of oscillation of the rod is2/