Problem 98. The drive mechanism imparts to the semicircular plate simple harmonicmotion of the form 0 = 0osinwot, where 0o is the amplitude of the oscillationand wo is its circular frequency. Determine the amplitudes of the angular velocity andangular acceleration and state where in the motion cycle these maxima occur. Note thatthis motion is not that of a freely pivoted and undriven body undergoing arbitrarilylarge-amplitude angular motion.O

Answered: Problem 98. The drive mechanism imparts…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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14. For the system shown to the right, the disk of mass m rolls without slip and z measures the displaccment of the disk from the unstretchcd position of the spring. 3k a) find the cquations of motion; b) if the system is inderdamped, whiat is the frequency of the frec vibrations of this system in terms of the parancters k, с, and m;
Problem 6: An object of mass 2 kg is attached to a spring of stiffness 200 N/m on a horizontal frictionless surface. Then it is extending by 10 cm and then let free to oscillate. 1- How long will it take to make one complete oscillation? 2- Determine the amplitude and give an expression for the displacement as a function of time. 3- Calculate its displacement, velocity, acceleration and force acting on it after sec. 4- Calculate its velocity by the time it is extended by 0.5 cm.
The following vibration system oscillates with a small angle. x = 0.6m, y = 1.8m, k = 18N/m. From the motor: static deflection = 0.2m, forcing frequency = 30 rad/s. If the starting angle from rest is 2 radians (counter-clockwise) and mass A is 10 kilograms, determine: 1. The natural frequency in radians per second. 2. The natural period in second 3. The amplitude of free vibration in meters (reference: neutral position of the spring below), 4. The amplitude of steady-state vibration in meters (reference: neutral position of the spring below) 5. The magnification factor 6. The overall displacement in meters when t= 1 second (reference: neutral position of the spring below).
An automobile whose weight is 150 N and it is mounted on 4 identical springs due to its weight it sags by 250 mm . each shock absorber has damping coefficient of 0.4 N for a velocity oof 30 mm/sec. The car is placed on a platform which moves vertically at resonance speed having an amplitude of 10mm. Find the amplitude of the car
A body vibrating with viscous damping makes five complete oscillations per second, and in 10 cycles its amplitude diminishes by 1/5 of the orginal value. Determine the logarithmic decrement and the damping ratio.
When a tree branch bends, it can be assumed that acts as a spring, i.e there is a restoring force −kx in response to a vertical deflection x. Internal friction of wood provides the dominant cushioning and is independent of the hanging mass, that is, F = −bẋ with b constant. We observe that a monkey of mass m1 hangs from the branch. East monkey oscillates many times, up and down before damping off appreciably, and coming to equilibrium. Then a second monkey of mass m2 hangs from the first monkey, and we observe that the monkeys together also oscillate several times before the branch reaches equilibrium. So the new equilibrium position of the branch is three times larger than with a single monkey. Besides, the energy loss per cycle for a monkey is half that of the loss with two monkeys. Based on these observations, determine the mass of each monkey (m1 and m2) in terms of a elastic constant k of the branch and a friction coefficient of the wood b. (Note: k and b are data)
A point mass is executing simple harmonic motion with an amplitude of 10 mm and frequency of 4 Hz. The maximum acceleration (m/s2 ) of the mass is
Find the new amplitude of oscillations of the block plus putty VA . A block of mass M attached to a spring of constant k, oscillates back and forth with amplitude A. At the instant shown, the block is at its maximum amplitude and a lump of putty of mass m is dropped from a small height sticking to the block. The mass of the spring is negligible and Putty Equilibrium Position the surface on which M moves is frictionless. M Find the new amplitude of oscillations of the block plus putty system. What is the new frequency of oscillations?
A single cylinder engine can be treated as a rotating unbalance model where the mass of the piston, m, acts at an eccentric distance, e which is half of the stroke. Determine the displacement amplitude of the engine in millimetres when it is rotating at a speed of 344.4 rpm. The engine parameters are: Mass of engine, M = 447.8 kg; keq = 220.3 kN/m; ceq = 2843.2 Ns/m; m = 10.6 kg and Stroke (i.e. 2e) = 236 mm. Give your answer to 2 dp. Answer:
A glider of mass 0.350 kg is placed on a frictionless, horizontal air track. One end of a horizontal spring is attached to the glider, and the other end is attached to the end of the track. When released, the glider oscillates in SHM with frequency 4.15 Hz. Find the period of the motion. Find the angular frequency of the motion. Find the force constant kk of the spring. Find the magnitude of the force that the spring exerts on the glider when the spring is stretched by 0.0200 m.
the Disc shown in the system has a mass of (4 m), and a radius of (r) the system undergoes a harmonic oscillation determine the followings: 1) the governing equation. 2) Natural and damped Frequency. 3) the response of the system after 3 s if the system has an initial velocity of 1 m/s. [providing that m-5 Kg, r=0.2 m, C=150 N-s/m, and K=500 N/m]. *
A 1.5 kg mass is attached to a vertically oriented spring, stretching it 0.45 m. The mass is moved upwards 0.25 m from its equilibrium position and held. A 0.8 kg mass is added to the hanging mass and the total mass is released from rest. Calculate the amplitude of the oscilating motion with both the 1.5kg and .8kg masses. Then, calculate by what total amount is the spring stretched when the speed of the masses are three-fourths the maximum speed

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