Solved : SHM along x-axis;(d2x/dt2) + Ax =0

A point moves with SHM along an x-axis according to the equation

 

The period of this motion is...

Answer:

The question said that the motion is along x-axis, so it really means the (particle) move in x-axis in Cartesian graphics (moving from (-x,0) until (x,0)). moving forward backward forward backward repeatedly. If we plot the position of particle in x-axis toward time. the plot will be like this: where the x-axis is the position of the particle, and the y-axis is the time.

can you understand (imagine) what the question tell? Now the equation given, A is amplitude, a constant value. The differential of x toward t in 2nd order means it is acceleration of the particle. 

SO, when the particle in negative x position (left side), the Ax have max negative value but the acceleration have max positive value (positive because the particle is being accelerate, not decelerate, to right side).Max positive plus max negative resulting zero. (fulfilled the equation).

When the particle in y-axis position (0,0), the particle have max speed but zero acceleration, and the Ax also zero because the x (position) have zero value. Zero plus zero resulting zero (fulfilled the equation).

When the particle in positive x position (right side), the Ax have max positive value but the acceleration have max negative value (means it decelerate, or accelerated to left side). Max negative plus max positive resulting zero (fulfilled the equation).

And it keeps repeating, left mid right mid left mid right and so on. Now because the move is SHM then the acceleration can be substitute with SHM acceleration equation, and the x also can be substitute with SHM displacement equation. Below is the complete step of solution:

That's it.. hope it can help you and useful for you..

Happy Expressing..!!