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Concept explainers
Damped free vibrations can be modeled by a block of mass in that is attached to a spring and a dashpot as shown. From Newton’s second law of motion, the displacement x of the mass as a
where k is the spring constant and c is the damping coefficient of the dashpot. If the mass is displaced from its equilibrium position and then released, it will start oscillating back and forth. The nature of the oscillations depends on the size of the mass and the values of k and c.
For the system shown in the figure, m = 10kg and k = 25 N/m. At time t = 0 the mass is displaced to x =0.18 m and then released from rest. Derive expressions for the displacement x and the velocity v of the mass, as a function of time. Consider the following two cases:
(a) c= 3(Ns)/m. (b) c = 50(Ns)/m.
For each case, plot the position x and the velocity v versus time (two plots on one page). For case (a) take
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Chapter 11 Solutions
EBK MATLAB: AN INTRODUCTION WITH APPLIC
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- What is the magnitude of the moment done by the force about the "z-axis" in the following figure. A 4 m F = (60i -80j - 20k} N | 3 m 7 m 4 m 6 m 2 m Parrow_forwardI. IDENTIFICATION. 1. It is composed of several connected members that are either fixed or pin connected at their ends. 2. The internal force Q in the direction of the centroidal axis of the beam is called the 3. The internal force V in the direction perpendicular to the centroidal axis is referred to as the 4. If the deformations disappear and the structure regains its original shape when the actions causing the deformations are removed, the deformations are termed 5. The permanent deformations of structures are referred to asarrow_forwardThe inertia constant of two groups of machines, which swing together are M1 and M2. The inertia constant of the system is M1- M2 , M1 > M2 M]M2 / M1- M2 M1 + M2 M1- M2 / M1M2arrow_forward
- A particle start its motion from rest under the action of constant force. if the distance covered in first 10 second is S1 and that covered in the first 20 seconds is S2 then O S2=4s1 O S2=2s1 O S2=s1 O S2=3s1arrow_forward*12-4. Starting from rest, a particle moving in a straight line has an acceleration of 3 (2t 6) m/s, where t is in seconds. What is the particle's velocity whent 6 s, and what is its position when t 11 s?arrow_forward1: During an experiment based on magnetic force, you can take 60 turn rectangular coil with length 20.0cm and height 30.0 cm. The coil is hinged along the Y-axis and 1.27 A current is passing through coil suchthat its plane makes an angle 40o with magnetic field. How can you find the magnitude and direction ofthe rotational force on coil by a uniform magnetic field 5000 G directed in the positive X-direction?What are possible ways to rotate coil in opposite direction?arrow_forward
- 10: The value of B at H-0 in a Hysteresis curve is called A) Remanence. B) Coercivity. C) Magnetization. D) Porosity 11: Ferrites are a sub-group of A) Non-magnetic materials, B) Ferro-magnetic materials, C) Paramagnetic materials, D) Ferri-magnetic materials. . 12: Find the true statement. A) Most of the substances show ferromagnetism, B) The magnetic susceptibility of diamagnetic substances are temperature independent, C) Water is paramagnetic in nature, D) Typical domain size of a ferromagnetic material is I nm. 13: Mutual inductance between two magnetically coupled coils depends on A) Permeability of the core material, B) Number of turns of the coils C) Cross sectional area of their common core, D) All of the above. 14: Which of the following circuit elements will oppose the change in circuit current? A)Capacitance. B) Inductance, C) Resistance, D) All of the above. 15: If the current in one coil is steady, what happens to the mutual inductance? A) Zero, B) Infinity. C) Doubles, D)…arrow_forwardA charged particle in a magnetic field will experience a nonzero magnetic force when what is true? O It is at rest. O It is moving in any way. O It is moving, but only parallel to the magnetic field. O It is moving such that its velocity has a nonzero component perpendicular to the magnetic field.arrow_forwardWhich of the following is not the characteristic of a force? O The plane in which the force acts O Direction of the force O Magnitude of the force O Nature of the force Shear forces are indirect forces to cearch 正arrow_forward
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