Write the equation for simple harmonic motion (x-t),(v-t), and find v at t=2s and t=3s if the object is initially at the right extreme of origin and moving in the negative x-direction. (A=2cm, T=8s)

Explanation:

T = 8 s

angular frequency ω = 2π / T

= 2 π / 8

= π / 4

x ( t ) = A ( sinωt + π / 2 ) because initial phase difference is π / 2

= A cos ωt

= A cos π t / 4  

v = Aω sinωt

= 2 x π / 4 sinωt

= .5 π sinπt / 4

when t = 2

v = .5 π sinπ x 2 / 4

= .5 π x 1

= 1.57  cm /s

At t = 3 s

v = .5 π sin π x 3 / 4

= .5 π sin 135°

= .5 π / √ 2

= 1.11 cm /s

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