A ball of mass 4 kg is placed at the lower end of a vertical spring, whose constant of restitution is 9 N/m, where the damping force is negligible. At the instant t=0, the ball is 0.2 m below the equilibrium position, where it is given a downward velocity of 1 m/s. From that instant, an external force g(t) = 18 sint) in newtons is activated and intervenes in the system. Using the given information: Write a differential equation and conditions that describe the position of the ball at time t in seconds. Also find the position function for the ball at any time t in seconds and determine the speed of the ball when t= 1 seconds and the position at 5 seconds.
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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