Abuoy floating in the sea is bobbing in simple harmonic motion with period 2 seconds and amplitude 8 in. its displacement d from sea level at time t=0 seconds is 0 in, and initially it moves downward. (note that downward is the negative direction.) give the equation modeling the displacement d as a function of time t. d= ク

The equation of the displacement as a function of time is :

Step-by-step explanation:

Generally , A simple harmonic wave is a sinusoidal function that is it can be expressed in simple or terms.

Thus,

is the general form of displacement of a SHM.

where,

is the displacement with respect to the mean position at any time is amplitude is the natural frequency of oscillation () is the phase angle which indicates the initial position of the object in SHM ()

given,

Time period () = The natural frequency () and time period () is :

                               

∴

=

∴

the equation :

⇒                        ------1

since when ,

⇒                         ------2

where n is an integer ;

⇒since the bouy immediately moves in the negative direction , must be negative or c must be an odd multiple of .

⇒         ------3

where k is also an integer ;

the least value of ;

thus ,

the equation is :

A1/27 = A2/39 =>

A2 = A1*39/27

A2 = 711×39/27

A2 = 1027 m^2