Simple Harmonic Motion (1 Viewer)

[want2beSMART]

PROVE THAT, if the displacement x of a particle P is related to the time t by the equation x=3cos(2[pi]t), then the motion is simple harmonic and state the period.

(ii) DETERMINE the greatest displacement, velocity and acceleration
(iii) DETERMINE when the particle is first at x=1 1/2 and the acceleration then
(iv) EXPRESS v^2 in terms of x, and state te interval within which P is restricted

 

[Estel]

ii) 3, 6pi, 12pi^2
iii) solve x = 1.5 (simple enuff)
iv) differentiate twice and then find v^2 the usual way... solve v^2>=0 for domain

 

[want2beSMART]

yeah but how did you do it?

 

[Estel]

max value of 3cosblah is 3
when you differentiate you'll get -6pisinblah, and the max for that is 6pi
etc etc

 

[want2beSMART]

oh

i thought you had to draw the graphs...

 

[Estel]

lol don't do work you don't have to