# 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 #