3. The physical pendulum. (a) In class, we derived the formula for the frequency of the physical pendulum W= Mgl I (1) Show that the expression for the frequency of the simple pendulum is consistent with this. Then derive (1) using the energy method, where the total energy is the sum of the rotational kinetic energy 1/1 (de/dt)2 and the potential energy of the centre of mass mghem. To obtain the result you will need to use the small angle expression for cosine: cos 01 02/2, for 0 <1. ― (b) A thin square plate of side L and mass M is hanging from a pivot that is drilled into one of its corners. The pivot passes perpendicularly through the plate. The plate is then lightly tapped and starts to undergo small oscillations. Using the energy method, determine the period of the oscillation, making the small angle approximation. The moment of inertia for an axis running through the centre of a square plate is ICM = ML²/6.

3. The physical pendulum. (a) In class, we derived the formula for the frequency of the physical pendulum W= Mgl I (1) Show that the expression for the frequency of the simple pendulum is consistent with this. Then derive (1) using the energy method, where the total energy is the sum of the rotational kinetic energy 1/1 (de/dt)2 and the potential energy of the centre of mass mghem. To obtain the result you will need to use the small angle expression for cosine: cos 01 02/2, for 0 <1. ― (b) A thin square plate of side L and mass M is hanging from a pivot that is drilled into one of its corners. The pivot passes perpendicularly through the plate. The plate is then lightly tapped and starts to undergo small oscillations. Using the energy method, determine the period of the oscillation, making the small angle approximation. The moment of inertia for an axis running through the centre of a square plate is ICM = ML²/6.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

. Explain the concepts of phase equilibrium with an example. Can you please help me for this question? I want a clear solution for me to understand
Please help me to solve this
3. The physical pendulum. (a) In class, we derived the formula for the frequency of the physical pendulum W3 Mgl I (1) Show that the expression for the frequency of the simple pendulum is consistent with this. Then derive (1) using the energy method, where the total energy is the sum of the rotational kinetic energy 1/1 (do/dt) 2 and the potential energy of the centre of mass mghem. To obtain the result you will need to use the small angle expression for cosine: cos 01-02/2, for 0 < 1. (b) A thin square plate of side L and mass M is hanging from a pivot that is drilled into one of its corners. The pivot passes perpendicularly through the plate. The plate is then lightly tapped and starts to undergo small oscillations. Using the energy method, determine the period of the oscillation, making the small angle approximation. The moment of inertia for an axis running through the centre of a square plate is ICM ML²/6. =
For a simple harmonic oscillator with x = A sin ot write down an expression for the velocity. Please use II* II for products (e.g. B*A), "/" for ratios (e.g. B/A) and the usual "+" and "-" signs as appropriate (without the quotes). For trigonometric functions use the usual sin and cos, while for Greek letters such as w, use omega. Please use the "Display response" button to check you entered the answer you expect.
I'm doing calc1 by myself right now and not sure where to start with this problem: Here are the questions: An object attached to a spring swings vertically around its equilibrium position. The height of the object relative to its position of equilibrium is given by the following function: h(t)=(e^-(x/10)*100sin(x)-10cos(x))/101 *(See photo i have provided)* a) Give the object movement for the first 10 seconds. I know i can find the speed of an object if i have it's acceleration. But how do i find it's movement fom it's height? I have done the integral of the height's equation and it's -(100e^-(x/10)(20sin(x)+99cos(x))/10201+Constant b) Give the total distance traveled by the object during the first 10 seconds I would assume this is something along the lines of finding the final positition of the object and the initial position and substracting them? c) Give the total distance that will be traveled by the object from time t = 0. at this point i am clueless to what i should find I…
Mech 431 vibration
A mass m = 7 kg is attached to a spring having a force constant k = 137 N/m as in the figure. The mass is displaced from its equilibrium position and released. What is the angular frequency in rad/s? (please show me the work in detail)
Hand written asap.. I'll upvote... plzzz fast plzzzzzz
Chapter 15, Problem 072 A uniform circular disk whose radius R is 14.7 cm is suspended as a physical pendulum from a point on its rim. (a) What is its period? (b) At what radial distance r < R is there a pivot point that gives the same period? (a) Number Units (b) Number Units Click if you would like to Show Work for this question: Open Show Work
Clem now is bored. The life of a cat. She disengages and begins to to bat at the toy at the end of the line essentially making a pendulum system. We will be modeling it as a simple pendulum now. Assume in these questions the line remains massless and taut. stoy sy 3. Clem bats the string to where the end is up a distance of Ay from the ground. What is the tangential velocity of the string when it passes through the origin? This is the maximum speed. Write in terms of Ay, m,, 0, g, and other mathematical constants. (Note: you might not have all of these variables in your final answer) 1 4. What is the ma um angle it will reach given the speed you calculated from the previous problem? Write in terms of Ay, m,, 0, g, and other mathematical constants. (Note: you might not have all of these variables in your final answer and assume the angle remains small such that we are assumed to be in SHM)
Please help me with this questions. Show all your work and the appropriate units If you can please also help me out with But if you can just do the word problem
Computer Lab: Undamped Spring Use Part 1.7 of IDE Lab 9 to visualize how the potential and kinetic energies of a mass-spring system change during an oscillation but maintain a constant total energy. • L i n e a r O s c i l l a t i o n s : F r e e R e s p o n s e Lab 9 clarifies the energies.