Please solve part d. Thank you for your help!!   An object is attached to the end of a vibrating spring and its displacement from its equilibrium position is y = 8e-t/2sin 4t, where t is measured in seconds and y is measured in centimeters. a. Graph the displacement function together with the functions y = 8e-t/2 and y = -8e-t/2. How are these graphs related? b. Use the graph to estimate the maximum value of the displacement. Explain whether or not it occurs when the graph touches the graph of y = 8e-t/2. c. What is the velocity of the object when it first returns to its equilibrium position? d. Use the graph to estimate the time after which the displacement is no more than 2 cm from equilibrium.

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Wave Motion

A wave motion is defined as the propagation of disturbances or transfer of energy and momentum from the state of rest or equilibrium to another point in a medium without any actual transfer of matter between them. In a simple explanation, it is the propagation of energy through a medium that is produced due to the repeated vibrations of the particles. Common things we see day to day like waves on water oscillation of a pendulum or bell, light wave, and all the subatomic particles exhibiting wavelike properties. The propagation of waves depends on the medium and their properties. The wave function is the disturbance that produces waves as a function of time. This disturbance oscillates periodically with a fixed frequency and wavelength. There are linear wave motion and non-linear wave motion based on their propagation, motion, and time period where linear wave motion is like sinusoidal waves and non-linear wave motion like a wave motion that gets interrupted in the middle of their propagation.