Question: A physical pendulum is formed by a rod of mass m and length 2L, at the ends there are two masses 2m and m are

A physical pendulum is formed by a rod of mass m and length 2L, at the ends there are two masses 2m and m′ are arranged, as shown in the attached figure. The axis of oscillation is horizontal and crosses the rod perpendicularly at its geometric center (E).

a) Determine the energy of the oscillating pendulum and, from this, find the equation of motion of the SHM.

b) While the pendulum is oscillating, the mass m′ is released from the rod. It is observed that the resulting pendulum registers an oscillatory motion whose frequency is just twice the original frequency. Calculate the value of the mass m′.
c) The mass m′ after falling is replaced by another mass 2m which is fixed at a distance x < L from the axis. Verify if there exists a position x that allows to have oscillations of minimum period m

2m E m m'

Step by Step Solution

★★★★★

3.51 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Page No Date ml by Ta is replaced man 2m at n42 I 1 ml ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Physics Questions!

A thin uniform rod of mass M and length L is bent at its center so that the two segments are now perpendicular to each other Find its moment of inertia about an axis perpendicular to its plane and...

A uniform rod of mass M and length L can pivot freely (i.e. we ignore friction) about a hinge attached to a wall, as in Fig. 8-54. The rod is held horizontally and then released. AT the moment of...

A uniform slender rod of mass m and length 4r rests on the surface shown and is held in the given equilibrium position by the force P. Neglecting the effect of friction at A and C, (a) Determine the...

Solve Prob. 18.23, assuming that the assembly is hit at B in a direction opposite to that of the z axis. Problem 18.23 Three slender homogeneous rods, each of mass m and length d, are welded together...

A rod of mass m and length L rests on two pulleys A and B which rotate in opposite directions as shown. Denoting by k the coefficient of kinetic friction between the rod and the pulleys, determine...

Figure shows a hollow cylinder of mass M = 1.2 kg and length L = 1.6 m that is free to rotate about a vertical axis through its center. Inside the cylinder are two disks, each of mass 0.4 kg that are...

Two particles, with charges of 20.0 nC and - 20.0 nC, are placed at the points with coordinates (0, 4.00 cm) and (0, -4.00 cm), as shown in Figure P25.28. A particle with charge 10.0 nC is located at...

Figure shows a hollow cylinder of length 1.8 m, mass 0.8 kg, and radius 0.2 m. The cylinder is free to rotate about a vertical axis that passes through its center and is perpendicular to the...

A uniform rod of weight Fg and length L is supported at its ends by a frictionless trough as shown in Figure P12.52. (a) Show that the center of gravity of the rod must be vertically over point O...

Protons having a kinetic energy of 5.00 MeV are moving in the positive x direction and enter a magnetic field B = 0.050 0kË T directed out of the plane of the page and extending from x = 0 to x...

CGT Co.s stock is currently selling for $15.25 per share, and they have 10,000,000 shares outstanding. They have $40,000,000 book value of 20-year, 9% coupon semiannual bonds outstanding (40,000...

use the income to calculate GDP in the approach economy of Spain where consumption = 5 billion euros, total wages for the entire economy are 4 billion, investment = 2 billion euros, Spanish firms...

Lim ( x ^ 2 ) / ( 1 - cosx ) as x approaches zero

What types of strategies would you recommend for an organization that achieves total weighted scores of 3.6 on the IFE and 1.2 on the EFE Matrix?

How would application of the strategy-formulation framework differ from a small to a large organization?

Do you believe the reasons to disclose by-segment financial information offset the reasons not to disclose by-segment financial information? Explain why or why not.

Give an example of equifinality as defined in the chapter.

Define problem recognition. How is this process like translating text from one language into another? What role does probing play in this process?

et's consider the situation of dropping a ball. Think about the forces acting on the ball while you are holding it in your hand, and then at different times after you have dropped it. What should the...

Post Lab: Data/Ca'CUIatiOns , , .,, Part 2 Physical Pandulum WU I. W Y , 1. Mean Farina,\" HAM mm. (,1 c, '11 '1?\" \\5 Part 2 Mass on Spring A Part 2 Mass on Spring B 1. Mass of 50 g or 100 g: 30 3...

Please answer Analysis #2 and #4. Also, please explain why the % difference is not within 0.2% in #2. E.g. If I: = 119.36 s, then 111 3 213363560 = 57.09639050illati0ns. However, since m must be an...

Please answer Analysis # 2 and 4. E.g. If I: = 119.36 s, then 111 3 213363560 = 57.09639050illati0ns. However, since m must be an integer, we take m = 57 since it is the closest integer. 9. Now,...

Please answer Analysis #1 and #6 THE PHYSICAL PENDULUM Object: To determine the acceleration of gravity g, and the radius of gyration of a bar k, together with their estimated random errors. Required...

plz solve all physics questions: 1. measuring the period of a pendulum T, would it be better to use 10 swings or 2 swings? Why? 2. If the value of is 5.2 0.2 seconds, what is the uncertainty in T 2 ?...

In class, we derived the formula for the frequency of the physical pendulum Mgl I = (1) Show that the expression for the frequency of the simple pendulum is consistent with this. Then derive (1)...