1.

A particle executes `SHM` represented by the equation, `y = 0.02 sin (3.14t+(pi)/(2))m`. Find (i) amplitude (ii) time period (iii) frequecy (iv) epoch (v) maximum velocity and (vi) maximum acceleration.

Answer» Compare the equation `y = 0.02 sin (3.14t+(•)/(2))`
with the general form of the equation,
`y = A sin (•t+•)`
(i) Amplitude `A = 0.01m`
(ii) Timw period is given by
`T = (2•)/(•)`or `T=(2•)/(3.14) = 2s`
(iii) Frequecny `f = (1)/(T) = (1)/(2) Hz = 0.5 Hz`
(iv) Epoch `• =(•)/(2) = (3.14)/(2) = 1.57 rad`
Epoch is initial phase
(v) Maximum velocity
`v_(max) = A• = 0.02 xx 3.14 = 0.0628 ms^(-1)`
(vi) Maximum acceleration
`a_(max) = A•^(2) = 0.02 xx (3.14)^(2) = 0.197 ms^(-2)`


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