- #1

Stealth849

- 38

- 0

## Homework Statement

A child on a 4m long swing is pulled back 1m from the vertical and released with a push imparting a speed of 2m/s. Find an expression for the angle θ, as a function of time, identifying the frequency ω, amplitude θi, and phase constant δ.

## Homework Equations

θ = θmax*cos(ωt + δ)

ω = √g/l

## The Attempt at a Solution

I got a value for omega, from √g/l, of 1.565

The fact that the child starts with initial velocity is really throwing me off. In order to find the phase constant, I've tried looking at equations

v = -ωθ*sin(δ)

θ = θi*cos(δ)

and solving for tan(δ) to get a value for δ of 3.17rad...

I don't even know if this is valid, but I otherwise don't know where to start.

I know that if the child is starting from an angle of 0.253rad with initial velocity, he should travel passed the point where I can use small angle approximation.

I thought also about differentiating the basic equation for harmonic motion θ = θmax*cos(ωt + δ) to get velocity, and setting that velocity equal to 2 at time 0, but there are still two unknowns. Any help will be appreciated. Thanks!