Question

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).

Answer 1

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 =
`(1.5)/(3.2)` = 0.4687

α =
`sin^(-1)(0.46875)` = 27.95° = 0.488 radian

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

d = 3.2sin(100πt ± 0.488 )