An object oscillates as it moves along the x-axis. Its displacement varies with time according to the equation (see description for full problem)

Question

An object oscillates as it moves along the x-axis. Its displacement varies with time according to the equation x=4sin(pi t + pi/6) where t=time in seconds and x=displacement in meters What is the displacement between t=0 and t=1 second?

Answer 1

X = 4 Sin( pi t +pi/6)

At t= 0

X₀ = 4 Sin(pi/6) = 4* Sin 30 = 2 m

At t= 1 s

X₁ = 4 Sin ( pi +pi/6)

= 4 Sin ( 7pi/6) = 4 Sin 210 = 4* (-1/2) = -2

Displacement = 2-(-2) = 4m