Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is at its maximum at time
t = 0.
amplitude 90 ft, period 0.5 min

Question

Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is at its maximum at time 
t = 0.
amplitude 90 ft, period 0.5 min

irishboy123 · Answer

the function you are looking for is 

y(t) = A cos wt 

A is the amplitude 90 ft.  ***note that cos w(0) - 1 so "the displacement is at its maximum at time t = 0" is satisfied.

w (it's actually the lower case Greek "omega") is the angular velocity in this most common recitation of the formula.  but you can relate w to  period T by noting that w = 2π/T.

anonymous · Answer

okay I got that far but I get confused as to what to do next

anonymous · Answer

@IrishBoy123

irishboy123 · Answer

that's the function, just plug in the values and post here

anonymous · Answer

so 90cos(4pi)?

anonymous · Answer

@IrishBoy123

irishboy123 · Answer

don't forget "t" in the equation:

y(t) = so 90cos(4π t)?

this is a time dependent oscillation!

also be sure to use the right units.  here you are using feet and minutes.  as long as everyone knows that, fine.