Classical Dynamics Of Particles And Systems
5th Edition
ISBN: 9788131518472
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning India
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Chapter 12, Problem 12.10P
To determine
The proof that normal coordinates have resonance corresponding to characteristic frequencies
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Classical Dynamics Of Particles And Systems
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- The shock absorbers for a new Proton X-50 car with mass 1000 kg unfortunately has some defects. The car sinks 3.0 cm when a person with 850 N weight climbs into the car at its center of gravity. Then, when the car hits a bump on the road while it is moving, the car starts oscillating up and down in simple harmonic motion. i. Calculate the period and the frequency of the oscillation. 11. 111. Now, if the absorbers were to be replaced, calculate the damping constant, b for the absorbers so that the car will be critical damped. Continue from Part ii above, if another passenger with the same weight of 850 N board the car, determine if the absorbers are still critically damped? If not, is it underdamped or overdamped? Explain.arrow_forwardProblem 5: Consider a 1D simple harmonic oscillator (without damping). (a) Compute the time averages of the kinetic and potential energies over one cycle, and show that they are equal. Why does this make sense? (b) Show that the space averages of the kinetic and potential energies are (T)₂ = k1² KA² and (U),= KA². Why is this a reasonable result?arrow_forwardObtain the solution for Eq. (12.62) for the forced harmonic oscillator using Laplace transforms.arrow_forward
- 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.arrow_forwardProb.1 (i) State the required conditions of simple harmonic motion (SHH). (ii) Consider the torsional pendulum with a moment of inertia I and torsion constant K. If the pendulum starts its oscillation with an initial angle O, and angular at t = 0. Obtain the equation of motion and angular frequency of dt de velocity j %3D oscillation w. for this pendulum and discuss that it can be classified as SHH. Show that the torsional angle and angular velocity a of the pendulum for all time can be expressed as (iii) sin wt 0 (t) = 0; coS wt + w(t) = -w0; sin wt + w cos wt .arrow_forwardplz answer asaparrow_forward
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