The suspension system of a mass M automobile \"sags” a distance x when the chass
ID: 1991580 • Letter: T
Question
The suspension system of a mass M automobile "sags” a distance x when the chassis is placed on it. Also, the oscillation amplitude decreases by a factor N each cycle. Estimate the values of (a) the spring constant k and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming each wheel supports an equal fraction of the weight. Make the simplifying assumption that the change in the period due to damping can be ignored. Express your answer in terms of the variables given and g.Explanation / Answer
The suspension system of a mass M automobile "sags” a distance x when the chassis is placed on it. Also, the oscillation amplitude decreases by a factor N each cycle. Estimate the values of (a) the spring constant k and (b) the damping constant b for the spring and shock absorber system of one... In our daily life we come across various kinds of motions. You have already learnt about some of them, e.g. rectilinear motion and motion of a projectile. Both these motions are non-repetitive. We have also learnt about uniform circular motion and orbital motion of planets in the solar system. In these cases, the motion is repeated after a certain interval of time, that is, it is periodic. In your childhood you must have enjoyed rocking in a cradle or swinging on a swing. Both these motions are repetitive in nature but different from the periodic motion of a planet. Here, the object moves to and fro about a mean position. The pendulum of a wall clock executes a similar motion. There are leaves and branches of a tree oscillating in breeze, boats bobbing at anchor and the surging pistons in the engines of cars. All these objects execute a periodic to and fro motion. Such a motion is termed as oscillatory motion. In this chapter we study this motion. The study of oscillatory motion is basic to physics; its concepts are required for the understanding of many physical phenomena. In musical instruments like the sitar, the guitar or the violin, we come across vibrating strings that produce pleasing sounds. The membranes in drums and diaphragms in telephone and speaker systems vibrate to and fro about their mean positions. The vibrations of air molecules make the propagation of sound possible. Similarly, the atoms in a solid oscillate about their mean positions and convey the sensation of temperature. The oscillations of electrons in the antennas of radio, TV and satellite transmitters convey information.
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