A mass of 1 slug is attached to a spring whose constant is 25 / 4 lb / ft. Initially the mass is released 1 ft above the equilibrium position with a downward velocity of 3 ft / sec, and the subsequent motion takes place in a medium that offers a damping force numerically equal to 3 times the instantaneous velocity. An external force ƒ(t) is driving the system, but assume that initially ƒ(t) K 0. Formulate and solve an initial value problem that models the given system. Interpret your results.
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.
A mass of 1 slug is attached to a spring whose constant is 25 / 4
lb / ft. Initially the mass is released 1 ft above the equilibrium position
with a downward velocity of 3 ft / sec, and the subsequent
motion takes place in a medium that offers a damping force numerically
equal to 3 times the instantaneous velocity. An external
force ƒ(t) is driving the system, but assume that initially ƒ(t) K 0. Formulate and solve an initial value problem that models the given
system. Interpret your results.
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