Help with SHM Questionn! (1 Viewer)

[WildKoala]

The velocity vms^-1 of a particle moving in SHM along the x-axis is given by:

v^2 = -x^2 - 4x + 12

1. find acceleration of particle in terms of x
2. state centre and period of motion
3. what is the max speed of the particle

thankyou!

 

[hayabusaboston]

The velocity vms^-1 of a particle moving in SHM along the x-axis is given by:

v^2 = -x^2 - 4x + 12

1. find acceleration of particle in terms of x
2. state centre and period of motion
3. what is the max speed of the particle

thankyou!

1. divide both sides by 1/2, then d/dx(0.5v^2) gives u answer.
2. Complete square and put into form v^2=n^2(a^2-x^2), and use 2pi/n to find period. Centre is wats in brackets.
3. (lol not sure if this right, seem to have forgotten, but max speed is when acceleration equals zero right HeroicPandas?)

 

[braintic]

3. (lol not sure if this right, seem to have forgotten, but max speed is when acceleration equals zero right HeroicPandas?)

The v^2 function is quadratic. You should be able to find its maximum value with or without calculus.
You should also know that the max speed occurs at the centre of motion, which was found in part (ii).
Actually your solution for part ii is not the simplest - you can read off the centre and period (indirectly) from the answer to part (i).

 

[HeroicPandas]

1. Times both sides by 1/2, then d/dx(0.5v^2) gives u answer.
2. Complete square and put into form v^2=n^2(a^2-x^2), and use 2pi/n to find period. Centre is wats in brackets.
3. (lol not sure if this right, seem to have forgotten, but max speed is when acceleration equals zero right HeroicPandas?)

yeh v(max) is which acceleeration is zero or u can find the vertex