Determine its maximum angular displacement

[andric_mcneil]

1. Really Stuck here I've got the period but after that like i said I'm stuck

A simple pendulum having a length of 1.53 m and a mass of 6.74 kg is given an initial speed of 1.36 m/s at its equilibrium position. Assume it undergoes simple harmonic motion.
(a) Determine its period.
2.48 s
(b) Determine its maximum angular displacement.
°

Homework Equations

? θ = θmcos(ωt)
?

The Attempt at a Solution

A.I'VE GOT THE PERIOD BUT I CAN'T GET maximum angular displacement

 

[G01]

You need to show some work to get help here. I can't know what is confusing you if you don't show me where you are getting stuck. If your stuck at a point before you have done any calculations, then try answering these questions:

How did you find the period?

Can you give me a formula for the displacement/velocity of the pendulum?

Do you know what the problem is asking for when it says, "Maximum angular displacement?"

What is the velocity of the pendulum when it is at maximum angular displacement?

 

[ogb p]

.

The maximum angular displacement, θm, can be determined using the equation θ = θmcos(ωt), where ω is the angular velocity and t is the time. In this case, we can use the equation for simple harmonic motion, ω = 2π/T, where T is the period. Therefore, we can rewrite the equation as θ = θmcos(2πt/T).

To find the maximum angular displacement, we need to find the time at which the cosine function reaches its maximum value of 1. This occurs at t = T/4, or one quarter of the period. Therefore, we can plug this value into the equation to get θm = θ(T/4) = θ(2.48 s/4) = θ(0.62 s).

Since we do not have a value for θ, we can solve for it using the initial conditions of the pendulum. At the equilibrium position, the angular displacement is 0, so we can set θ = 0 and solve for θm.

0 = θmcos(2π(0.62 s)/2.48 s)

0 = θmcos(π/2)

0 = θm(0)

Therefore, the maximum angular displacement is 0 degrees. This makes sense, as the pendulum is given an initial speed at the equilibrium position and will only move in one direction, not reaching any maximum displacement.