A mass suspended from a helical spring of stiffness s, is displaced by a distance x from its equilibrium position and allowed to vibrate. Show that the motion is simple harmonic.
(a) A mass suspended from a helical spring of stiffness s, is displaced by a distance x from its
equilibrium position and allowed to vibrate. Show that the motion is simple harmonic.
(b) A vertical helical spring having a stiffness of 1540 N/m is clamped at its upper end and carries a
mass of 20 kg attached to the lower end. The mass is displaced vertically through a distance of
120 mm and released. Find : 1. Frequency of oscillation ; 2. Maximum velocity reached ; 3.
Maximum acceleration; and 4. Maximum value of the inertia force on the mass.
(c) A machine of mass 75 kg is mounted on springs and is fitted with a dashpot to damp out vibrations.
There are three springs each of stiffness 10 N/mm and it is found that the amplitude of vibration
diminishes from 38.4 mm to 6.4 mm in two complete oscillations.
Assuming that the damping force varies as the velocity, determine : 1. the resistance of the dashpot
at unit velocity ; 2. the ratio of the frequency of the damped vibration to the frequency of the
undamped vibration ; and 3. the periodic time of the damped vibration.
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