A spring is stretched 10 cm by a force of 3 N. (Note that by Hooke's law this means that F = kx where F = 3 N is force, x = 10 cm is displacement, and k is the spring constant.) A mass of 4 kg is hung from the spring and also attached to a damper that exerts a force in the direction opposite to the direction of motion of the mass with magnitude proportional to the speed of the mass. The damper exerts a force of 3 N when the speed is 6 m/s. If the mass is pulled 12 cm below its equilibrium position and given an initial downward velocity of 12 cm/s, find the position u (in m) of the mass at any time t (in s). (Assume that position is measured upward from the equilibrium position)
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
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