Question

An object's motion is described by the equation d=4sin(pi*t) . The displacement, d, is measured in meters. The time, t, is measured in seconds. Answer the following questions:
What is the object's position at t=0?
What is the object's maximum displacement from its resting position?
How much time is required for one oscillation?
What is the frequency?

Answer 1

Would love some help in completing but also understanding this. Thanks, Cheers!

Answer 2

Displacement d = 4 sin(t*Pi)
When t = 0, sin 0 = 0 and d = 0: the object is at starting point.
sin (t*Pi) varies from 0 to 1, to 0, then -1, then back to 0.
d varies from 0 to 4, to 0, then to -4, then back to 0. The max displacement is 8
After one oscillation, sin(t*Pi) = sin 2pi -> t*Pi = 2Pi -> t = 2 sec.
The frequency (or period) is 2Pi

Answer 3

Thanks!