y = yo cos wt l φ m A pendulum has a mass m connected by a rigid rod of length to a pivot point. An external force causes the pivot point to oscillate vertically, with y yo cos wt. Gravity is pointing downward. = a) [10 pts] Write the Lagrangian for the pendulum, in terms of the angular coordinate o.
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![y = yo cos wt
l
φ
m
A pendulum has a mass m connected by a rigid rod of length to a pivot point. An external
force causes the pivot point to oscillate vertically, with y yo cos wt. Gravity is pointing downward.
=
a) [10 pts] Write the Lagrangian for the pendulum, in terms of the angular coordinate o.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F26aae71d-c8c3-4690-8d08-493578d9bb1d%2F5f3d4926-66cd-44f3-bdd2-ed826bbaa69d%2Fb27msen_processed.jpeg&w=3840&q=75)
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- Need help on this question. The anwser should be 2.07Fill in each blank so that the resulting statement is true.O mr - 2mrre- mgr sin e wU A simple pendulum of length b and bob with mass m is attached to massless support moving vertically with constant acceleration a. The Lagrangian of the system is Select one: OL-m(a*e - 2atblcond + b") + OL-m(a* - 2atbésind + b0") + mgbaino OL=m(a* + 2atbbsind + P0) + mg(b cos-at") OL- m(a*t - 2atbdcose + 6*0) + mg(b sind-at"). zed coordinates you need to describe this system
- Apps Bookmarks pls.skillport.com U Registration/Login... Ú UltiPro U UltiPro Registration/Login. 0email TransNational Bank. magnitude 111.51 direction to the left Need Help? Talk to a Tutor Read It -/1 points V SERPSE8 23.P.010. A My Notes Ask Your Teacher V Two small metallic spheres, each of mass m = 0.192 g, are suspended as pendulums by light strings of length L as shown in the figure below. The spheres are given the same electric charge of 7.7 nC, and they come to equilibrium when each string is at an angle of e = 4.65° with the vertical. How long are the strings? L. т т Need Help? Talk to a Tutor Read It 1:37 AM 6) 3/24/2020 acer Pause Print Scm SYSRQ Scroll Lock F12 F10 F11 Break F8 F5 F6 F3 Page Up Num Lock Backspace Insert Home Page Down Delete End A WARNING Enter To reduce risk of serious injury read Safety & Comfort Guide provided with product and at www.hp.com/ergo TShift End Ctri Alt pmall 00 5.straight line is always acted upon by a force from the centre of the path and directed Ex. 2: A particle of mass 8 gm moving in a and maximum acceleration, if the amplitude is towards the centre. Find its maximum velocity sse magnitude is 128 times the displacement 5 cm.It is known that a general solution for the position of a harmonic oscillator is x(t) = C cos (wt) + S sin (wt), where C, S, and ware constants. (Figure 2) Your task, therefore, is to determine the values of C, S, and w in terms of k, m,and init and then use the connection between x (t) and a (t) to find the acceleration. Figure L min x=0 Xinit 1 of 2 > Part A Combine Newton's 2nd law and Hooke's law for a spring to find the acceleration of the block a (t) as a function of time. Express your answer in terms of k, m, and the coordinate of the block x (t). ► View Available Hint(s) a (t) = Submit 17 ΑΣΦ Part B Complete previous part(s) Review | Constants ?
- If you did the previous question right, you hopefully got an expression for yo. You may notice that you can simplify the differential equation a little bit: d'y k (y – yo) dt2 т The parameter yo now plays the roll of the "relaxed length". A better term may be "equilibrium value for y". But mathematically, it's identical to a relaxed length with the spring as the only force. We continue using this equation: y(t) = Y0 + A cos(wt + y) Now, solve for A (in cm) with these parameters. Again, if you need more information, enter -100000. The parameters are: •m = 200 grams • Yo = (equilibrium value) = 40 cm • k = (spring constant) = 0.03 N/cmneed asap pleaseTwo blocks and three springs are Configured below. All motion is honzental. when the blocks are aū jest spoings are unstretched: Kz k3 Suppse mi=2m mzzm, K,=4k okzz k, Ksz 2k. Find the charactesistics freguencies Foo Small oscillations.