Question

A mass suspended on a spring will exhibit sinusoidal (sine wave) motion when it moves. If the mass on a spring is
9 cm off the ground at its highest position and 1 cm off the ground at its lowest position and takes 4 seconds to go
from the top to the bottom and back again, determine an equation to model the data.

Answer 1

anyone can help me to do that :((((

Answer 2

your range is from 1 cm to 9 cm, so a = 4
period = 4 sec
2π/k = 4
k = π/2

our starting equation is
h = 4 sin π/2(t) + 5

assuming the min happens at t = 0, right now it happens at t=3
so we need:
h = 4 sin π/2(t + 3) + 5

check
t=0, h = 1
t = 1, h = 5
t = 2, h = 9
t = 3 , h = 5
t = 4 , h = 1 <--- back to start

looks good