Solving Simple Harmonic Motion for All Time

[jam12]

Homework Statement

I have that a oscillating mass undergoes shm. It is accelerated (forced oscillation) by 1ms^-2, for time pi/2 as it goes through the origin and then accelerated by -1ms^-2 for another time pi/2, then it is at the origin after the second acceleration.

I need to determine an expression for the acceleration for all time.

Homework Equations

None

The Attempt at a Solution

i can only think of something along the lines: f(t)= 1 0<t<pi/2
= -1 pi/2<t<pi
= 0 t>pi
but this is wrong as it only considers the acceleration for time 0 to pi. I need it for all time, since the mass will start accelerating (forced) when it travels past the origin to the other direction and continues to oscillate back and forth.

 

[viscousflow]

Look up Fourier series and something called the step function.

 

[jam12]

thanks, I've tried but its no use since i need a function that turns on and of and on etc an infinite number of times

 

[viscousflow]

When these two are combined you get something called a square sine wave. Check again

http://en.wikipedia.org/wiki/Square_wave

 

[jam12]

Looking at the squarewave function expression I see my function will be a sum of heaviside step functions? and i can change the period according to what i need.
Many thanks