Science

PhysicsQ&A Librarymass m is fixed toPendulum A simple pendulum consisting of a point1.the end of a massless rod (length /), whose other end is pivoted from the ceiling to letit swing freely in a vertical plane,specified by its angle o from the equilibrium position.(a) Prove that the pendulum's potential energy (measured from the equilibrium level) isas shown below. The pendulum's position can beU ()mgl (1 - cos )(b) Write down the total energy E as a function of and o. Show that by differentiatingyour expression for E with respect to t you can get the equation of motion for ¢ andthat the equation of motion is just the familiar Tmoment of inertia, and a is the angular acceleration ).(c) Assuming that the angle remains small throughout the motion, show that the motionis periodic with periodIa (where T is the torque, I is the- 2т V1/9.Tоm1 (d)To get the pendulum's period good for large oscillations as well as small,the following method: Use the above PE, findwe can usedoas a function of d. Next use11dtin the form tdo/o, to write the time for the pendulum to travel from ø = 0 to itsmaximum value (the amplitude) . Now show thatdu-Фdo2То -T TO1VI-u2I-A2u2sin (d/2) sin2 (ø/2)0is the period for small oscillation given above and A = sin(P/2). These inte-where Tograls cannot be evaluated in terms of elementary functions. However, the second integralis a standard integral called the complete elliptic integral of the first kind, sometimes de-noted K(A2), whose values are tabulated and are known to computer software such asMathematica, which calls it EllipticK (A2)].Question

Asked Oct 8, 2019

57 views

can you do part d please

Step 1

Write the expression for potential energy of the system.

Step 2

Write the expression for total...

Find answers to questions asked by student like you

Show more Q&A

Q: a 40 N horizontal force is applied to a 6.0 kg box. Friction is negligible. The box moves a horizont...

A: Work done is given by,

Q: A customer sits in an amusement park ride in which the compartment is to be pulled downward in the n...

A: (k) Projection of the apparent force according to the customer's measure of the coin's acceleration ...

Q: A ball is thrown horizontally from the top ofa building 130 m high. The ball strikes theground 74 m ...

A: Given:Height of the building, h = 130 mHorizontal range of the ball, s = 74 mInitial velocity of the...

Q: The question states:The hammer throw is a track-and-field event in which a 7.3-kg ball (the “hammer”...

A: The velocity at the time of release, is given by,

Q: 25.38 A battery-powered global positioning system (GPS) receiver operating on 9.0 V draws a curr...

A: Given values:Operating voltage, V = 9.0 VDrawn current, I = 0.13 A Consuming time, t = 30 min. = 30 ...

Q: 18. A bag of cement whose weight is F, Shangs in equilibrium from three wires as shown in Figure P5....

A: Write the components of the tension along vertical and horizontal direction. Take upward and right d...

Q: A small car gets into a head on collision with an 18-wheeler. During the collision, which vehicle ha...

A: Click to see the answer

Q: The coefficient of static friction between Teflon and scrambled eggs is about 0.029. What is the sma...

A: Given:Coefficient of friction between teflon and scrambled egg = 0.029

Q: Large telescopes often have small fields of view, i.e. it can only see a very small corner of the sk...

A: The field view of the telescope is 0.055 degree.The angular area of Hubble Space Telescope (HST) wil...