A particle is moving with SHM of period 16s and amplitude 10m. Find the speed of the particle when it is 6.0m from its equilibrium position.

Question

First I found the value of w:
w= 2 pi/ T
= 2 pie/ 16
=0.393 s^-1

Then I used:
v= +/- w root a^2 - x^2
= +/- 0.393 root 10^2 - 6^2
= 3.14 m/s

My problem is in the next question:

How far is the particle in question 1 from its equilibrium position 1.5s after passing through it? What is its speed at this time?

The answers should be 5.6m , 3.3m/s

Can someone help me please? Thanks!

Answer 1

You can represent displacement vs time as
X = 10 sin (0.393 t), where
t = 0 corresponds to an equilibrium position. The velocity will be
V = 3.93 cos (0.393t)
Substitute t = 1.5 s and you should get the right answers, after rounding off to two significant figures

Answer 2

woah. Will i have to learn this when i grow older?

Answer 3

Only if you choose to take physics in high school and/or college.