Question

Q5 Q19.) Choose the correct formula for the displacement d from the rest position of the object attached to the spring at time t. Show your details as to how you got your answer.

Answer 1

simple harmonic motion eqn: d = A*sin(wt + p) where d is displacement, A is amplitude, p is phase angle and w is angular velocity = 2pi/T where T is period

at t = 0, d = 0 so p = 0
at t = 0, it moves downward so d is negative
A = -2
w = 2pi/4.5 = 4pi/9

combining d = -2sin(4pi/9*t)
ans is D

Answer 2

t=0, d=0 so ans B is wrong

t=0, dd/dt <0 as it is propelled downward so ans C is wrong

ang vel = 2$\pi$ / period

= 2$\pi$ / 4.5

= 4$\pi$ / 9

so D is the correct answer