Question

A mass attached to a spring oscillates with a period of 3.26 s. If the mass starts from rest at x = 0.0410 m and time t = 0, where is it at time t = 3.27 s?

Answer 1

T = time period of oscillation = 3.26 s

w = angular frequency = 2pi/T = 6.28/3.26 = 1.93

A = amplitude = 0.0410

X = A Sin(wt + )

at t = 0

X = 0.0410 = A Sin

0.0410 = 0.0410 Sin

= 90

so equation becomes

X = A Sin(1.93t + /2)

at t = 3.27

X = (0.0410) Sin(1.93 (3.27) + 1.57)

X = 0.041 m