# Homework Help: Simple Harmonic Motion

1. Dec 3, 2011

### acmmanoj

I am having a question and tries to solve a problem for days. Consider general SHM. When the particle reaches to the maximum displacement, a if a velocity U is given to the particle towards to the center of SHM, (keeping the same force mω^2x)

1. What would happen to the SHM...is it same or can i use same equations or should i derive equation again

Should i consider this as new SHM ( X=a when t=0) or should i continue from same SHM (X=0 when T=0)

2. if i derive again, which point should i considered as center, what will happen to the displacement and maximum displacement...is it same or difference

3. when tries to get equation of motion as x=asin(ωt) from intergartion it produces a very complex equation. (in intergration i took, when x=a , v=u and x=a t=0)

2. Dec 3, 2011

### Simon Bridge

You are saying that when the pendulum reaches it's maximum displacement you give it a kick towards the center?

1. This ads energy to the system, resonantly.
This is no longer SHM - it is now a driven harmonic oscillator.

2. Without damping you are solving something like:

$$m\frac{d^2x}{dt^2}+kx=f(t)$$
... where f(t) is the applied force.

You can simulate a series of kicks by a sequence of Dirac-delta functions for the specific impulse. The center is still the same, the mass will come back further.

3. ... and yes, the equation can get quite complicated.

3. Dec 3, 2011