A particle is executing simple harmonic motion with time period of 4 s and amplitude 10 cm. Calculate displacement, velocity after `(1)/(2)` second starting from mean position.

Explanation

T = 3s, A = 10 cm, `t = (1)/(2)s`
(i) As x = A `sin omegat`
` = 10 sin (2pi)/(T)t`
` = 10 sin (2pi)/(4) xx (1)/(2)`
` = 10 xx (1)/(sqrt(2)) = 7.07` cm
`V = (dx)/(dt) = Aomegacos omegat`
` = A(2pi)/(T)cos (2pi)/(T)t`
` = 10*(2pi)/(4) cos (2pi)/(4) xx (1)/(2)`
` = 5pi cos (pi)/(4)`
` = (5pi)/(sqrt(2)) = 5 xx 3.14 xx 0.7`
` = 10.99` cm/s