A block of charge q and mass m is connected to a spring of constant k. An electric field E exists parallel to the ground. The block is released from rest from a unstreched spring. Find Maximum displacement?
1 Answer
Apr 29, 2018
Explanation:
Newton's 2nd law:
#F = ma#
Here:
#F = Eq - kx#
The spring linearly opposes displacement from the equilibrium position, hence the negative term and the harmonic oscillation.
Hence, equation of motion:
# implies ddot x + k/mx = (Eq)/m#
General solution:
#x = A cos omega t + B sin omega t + (Eq)/k# , where#qquad omega^2 = k/m#
With IV's:
#x(0) = 0#
#x'(0) = 0#
So the governing equation is:
# x = (Eq)/k (1- cos sqrt(k/m) t)#
Because
# 0 lt x lt (2Eq)/k #