# Pendulum question if a pendulums motion is shown ...?

by θ(t)=Zsin (ωt+P)

and the length of the pendulum is 1.2m and when t=0 it is released from rest at θ = 0.25 rad. How do you define equations for displacement θ in terms of t. Also for the angular velocty dθ/dt.

I can calculate ω given the above information, but i am still then left with the Z and P which i am not sure what to do with. Any help appreciated to get me on my way

Relevance
• Anonymous

θ(t )= Z sin (ωt+P)

dθ/dt = Zω cos (ωt+P)

initial condtion;

dθ/dt = 0 at t =0

Zω cos (ω(0)+P) = 0

Zω ≠ 0..................so cos (P) = 0

P = ½π (2n -1)..................n = 1, 2, 3, 4.............

let take n = 1.....so P = ½π

initial condtion;

θ = 0.25 at t =0

0.25= Z sin (ω(0) + ½π)

Z = 0.25

general solution

θ(t )= 0.25 sin (ωt + ½π)