A 16-lb weight is attached to a frictionless spring, that in turn is suspended from the ceiling. The weight stretches the spring ft and comes to rest in its equilibrium position. The weight is then pushed up 1 foot and released with an upward velocity of 6 ft/sec. Find the initial value problem that describes the motion of the weight, and solve it, writing your solution in the form u(t) = R cos( ω0t - δ )
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 16-lb weight is attached to a frictionless spring, that in turn is suspended
from the ceiling. The weight stretches the spring ft and comes to rest in its
equilibrium position. The weight is then pushed up 1 foot and released with an
upward velocity of 6 ft/sec. Find the initial value problem that describes the motion of
the weight, and solve it, writing your solution in the form u(t) = R cos( ω0t - δ )
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