Question

find a model for simple harmonic motion if the position at t=0 is 0 the amplitude is 5 centimeters and the period is 4 seconds

Answer 1

d = 5sin(πt)
hope this helped

Answer 2

y = 5sin
`((x)/(2))`

Explanation:

Since harmonic motion is represented by the sine wave equation.

y = a sin (bx)

where a = amplitude

period =
`(2\pi)/(b)`

Amplitude of the harmonic motion is given as 5 and period is 4 seconds.

so a = 5

and 4 =
`(2\pi)/(b)` ⇒ b =
`(2\pi)/(4)`

b =
`(\pi)/(2)`

Now we replace the values of a and b in the sine equation

y = 5sin
`((x)/(2))`