Question

A weight is suspended from a spring and is moving up and down in a simple harmonic motion. At start, the weight is pulled down 5 cm below the resting position, and then released. After 8 seconds, the weight reaches its highest location for the first time. Find the equation of the motion. 

Answer 1

General equation for simple Harmonic equation of spring is;

$X=$ A cos $(2\pi\>ft+\phi)$

$X=$ Displacement

$A=$ Amplitude $=0.05m$

$f=$ Frequency

$t=$ time

and $\phi=$ Phase angle

at $t=0,x=-5$

$\therefore-0.05=0.05\>cos(0+\phi)$

$\implies\phi=\pi$

Period time T $=8×2=16\>$ seconds

$f=\frac{1}{T}=0.0625$

$\therefore\>X=0.05\>cos(0.3927t+\pi)$