Differential equation A mass weighing 64 lb lengthens a spring by 0.32 f t. At the beginning the mass is released from a point that is 8 inches above the equilibrium position with a descending velocity of 5ft/s Find the equation of motion. . Plot position vs time. . What are the amplitude and period of the movement? . How many complete cycles will the mass have performed at the end of 3π seconds? At what point does the mass pass through the position of equilibrium with downward direction for the second time? At what moments does the mass reach its extreme displacements on either side of the equilibrium position? . What is the position of the mass at t = 3 s? . What is the instantaneous velocity at t = 3 s? i. What is the acceleration at t = 3 s? j. What is the instant speed in moments when the mass passes through the equilibrium position? k. At what moments is the mass 5 inches below the equilibrium position? At what moments the mass is 5 inches below the equilibrium position pointing upwards

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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.