Shm (1 Viewer)

[twistedrebel]

(a) if x=asin nt + b cos nt find the acceleration of the particle in terms of t, and show that a=-n^2 x
(b)find the amplitude and period of the motion
(c) find the maximum velocity

 

[addikaye03]

(a) if x=asin nt + b cos nt find the acceleration of the particle in terms of t, and show that a=-n^2 x
(b)find the amplitude and period of the motion
(c) find the maximum velocity

x=asin nt + b cos nt

dx/dt=nacos(nt)-bnsin(nt)

d^2x/dt^2=-n^2asin(nt)-n^2bcos(nt)

=-n^2[asin(nt)+bcos(nt)]

=-n^2x as requires

B) Hint: Velocity = 0 at maximum displacement & T=time for one oscillation
ie. Time from a max displacement to another max displacement
So that makes that question pretty easy (need more help, let us know)

c) Hint: Max Velocity occurs through equilibium position, that is, centre position over which the particle oscilates, find x then find v at that point.

 

[shaon0]

x=asin nt + b cos nt

dx/dt=nacos(nt)-bnsin(nt)

d^2x/dt^2=-n^2asin(nt)-n^2bcos(nt)

=-n^2[asin(nt)+bcos(nt)]

=-n^2x as requires

B) Hint: Velocity = 0 at maximum displacement & T=time for one oscillation
ie. Time from a max displacement to another max displacement
So that makes that question pretty easy (need more help, let us know)

c) Hint: Max Velocity occurs through equilibium position, that is, centre position over which the particle oscilates, find x then find v at that point.

You could just make them into one equation using auxillary. Then everything's easy from then on.

 

[addikaye03]

You could just make them into one equation using auxillary. Then everything's easy from then on.

Yeah true... haven't thought auxillary in ages. I do alot of SHM in physics these days... I view it heaps diff than i did at school. You're right though.