An oscillating mechanism has a maximum displacement of 3.2m and a frequency of 50hz. at timet-0 the displacement is 150cm. express the displacement in the general form asin(wt + α).

Given:

max displacement, A = 3.2 m

f= 50 Hz

at t = 0, displacement, d = 150 cm = 1.5 m

Solution:

Displacement in the general form is represented by:

d = Asin(ωt ± α)

d = 3.2sin(2πft ± α)

d = 3.2sin(100πt ± α)                    

where,

A = 3.2 m,            

ω = 2πf = 100π

Now,

at t = 0,

1.5 = 3.2sin(100π(0) ± α )

1.5 = 3.2sinα

sin α = = 0.4687

α = = 27.95° = 0.488 radian

Now, we can express displacement in the form of 'Asin(wt + α)' as:

d = 3.2sin(100πt ± 0.488 )

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