The equation of linear SHM is x= 10`sin ( 4pi t + pi/6)` cm. Find the period and maximum speed of the motion.

Explanation

Data : x = ` 10 sin ( 4 pit+ pi/6) ` cm ltbr In the usual notation, the expression for displacement of a particle in linear SHM is
` x = A sin (omega t+ prop)`
Comparing this equation with the given equation , we get,
` A =10 cm, m omega = 4 pi "rad/s" prop = pi/6 " rad"`
Therefore, (i) The period , ` T= (2pi)/omega = (2pi)/(4pi) = 0.5 s `
(ii) The maximum speed,` v_(max) = omegaA= (4 pi") (0.1)`
= ` 0.4 xx 3.142`
= 1.2568 m/s