Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Write the equations that describe the simple harmonic motion of a particle moving uniformly around a circle of radius8units, with linear speed 3units per second.
The equation of motion for a damped harmonic oscillator is s(t) = Ae^(−kt) sin(ωt + δ),where A, k, ω, δ are constants. (This represents, for example, the position of springrelative to its rest position if it is restricted from freely oscillating as it normally would).(a) Find the velocity of the oscillator at any time t.(b) At what time(s) is the oscillator stopped?
Two springs of force constants k1 and k2 are attached to a block of mass m and to fixed supports as shown in Fig. 2. The table surface is frictionless.
(a) If the block is displaced from its equilibrium position and is then released, show that its motion will be simple harmonic with angular frequency w = √(k1 + k2)/m.
(b) Suppose the system is now submersed in a liquid with damping coefficient b , what is the condition that the block will return to itsequilibrium position without oscillation?Sketch a graph to show the behavior of the system in this case.
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