Question

The position of a SHO as a function of time is given by x = 7.1cos 7πt  + π 

                          3      6

where t is in seconds and x is in centimetres. Find:

a)               the period and frequency expressed as fractions                        

b)              the velocity at t = 2.5 (to 2 sig. fig.)                                            

 

Answer 1

$x=7.1\cos(7\pi t+\pi/36)$. So, we have

a) $T=2\pi/\omega=2\pi/(7\pi)=2/7\ (s)$

$f=1/T=1/(2/7)=7/2\ (Hz)$

b) $v=dx/dt=-1.56\cdot\sin(7\pi t+\pi/36)$

$v(2.5)=-1.56\cdot\sin(7\pi \cdot2.5+\pi/36)=-1.6\ (m/s)$