A child, standing in a swing, bends her knees and then straightens them twice per swing period,
Question:
A child, standing in a swing, bends her knees and then straightens them twice per swing period, making the distance ℓ from the swing’s support to her center of mass oscillate as
is the swing’s mean angular frequency.
(a) Show that the swing’s angular displacement from vertical, θ, obeys the equation of motion
where ω1 = √gℓ1, and θ is assumed to be small, θ «1.
(b) Write θ = X1 cos ω0t + X2 sin ω0t .Assuming that ℓ1 « ℓ0 so ω1 « ω0, show that the child’s knee bending (her “pumping” the swing) squeezes X1 and amplifies X2 (parametric amplification):
(c) Explain how this squeezing is related to the child’s conscious manipulation of the swing (i.e., to her strategy for increasing the swing’s amplitude when she starts up, and her strategy for reducing the amplitude when she wants to quit swinging).
Step by Step Answer:
Modern Classical Physics Optics Fluids Plasmas Elasticity Relativity And Statistical Physics
ISBN: 9780691159027
1st Edition
Authors: Kip S. Thorne, Roger D. Blandford