Trigonometry question

Question

Suppose an object attached to a coiled spring is pulled down a distance of 18 in from its rest position and then released. If the time for one oscillation is 11 sec, develop a model that relates the displacement d(t) of the object from its rest position after time t (in seconds). Assume no friction.

d(t)=

Answer 1

Since it says there is no firction, the mostion is simple harmonic. And based on the given information:

1. Amplitude of 18 in,
2. Time Period of 11 sec,
3. Relased from macimum displacement would be using cosine,
4. and will be using the displacement measured from the rest position.

Step 1: Angular frequency

1. ω = 2π/T = 2π/11

Step 2: Model form

1. d(t) = A cos (ωt)

That means that the final model is: d(t) = 18 cos (2π/11 t)