Classical Mechanics - Hooke's Law

A particle is constrains to move along the x-axis under the influence of the net force F = − kx with amplitude A and frequency f, where k is a positive constant. When x = A/2, the particle speed is

A. 2πfA
B. √3πfA
C. √2πfA
D. πfA
E. (1/3) πfA

(GR8677 #77)

Solution:



Equation of motion:
with angular velocity: ω = √(k/m) = 2πf

Solution to the equation of motion, wave function: x = A sin ωt
Velocity: v = dx/dt = Aω cos ωt

x = A/2 → A sin ωt = A/2
sin ωt = 1/2 → ωt = 30^o
cos 30^o = ½√3

v = Aω cos ωt = A 2πf  ½√3 = √3πfA


Answer: B