physics - Solving a SHM (Simple Harmonic Motion) with given velocities at specific time -

shm - simple harmonic motion

a simple harmonic oscillator has frequency of 6.2 hz. oscillating along x, x(t) = acos(wt + d). given velocity @ 2 moments: v(t=0) = 1.9 cm/s , v(t=.1) = -19.4 cm/s.

calculate , d.

since know t = 1/f, found out t = 0.1612 , since, w = 2pi / t, w = 38.9557

can't find out velocities ?!

need possible...

you

v(t) = -a*w*sin(w*t+d)  

and know v(0)=-aw*sin(d) v(t) t=0.1.

v(t) = x'(t) = -a*w*( cos(w*t)*sin(d)+sin(w*t)*cos(d) ) 

so

-a*w*cos(d) = ( v(t)-cos(w*t)*v(0) ) / sin(w*t) 

and conversion polar coordinates give values a , d.