hsc 1997 2b) (1 Viewer)

[gunat61]

find the maximum acceleration of the particle for:
x = 3sin(2t+5) ... the answers are not clear to me and neither am i getting it lol =/

thanks

 

[b3kh1t]

find the maximum acceleration of the particle for:
x = 3sin(2t+5) ... the answers are not clear to me and neither am i getting it lol =/

thanks

First you need to find the equation for acceleration, which is .







Therefore it can be seen from the equation that the maximum value for the acceleration is 12 m/s^2.

 

[cssftw]

max acceleration occurs when particle is at the end points of motion, i.e. x = 3 or x = -3

you know x'' = -n^2(x) = -4x

so sub in x = -3

max acceleration = 12 m/s/s

 

[gunat61]

LOL right .. it makes sense now haha the answers confused me. thanks guys!

 

[gunat61]

First you need to find the equation for acceleration, which is .









Therefore it can be seen from the equation that the maximum value for the acceleration is 12 m/s.

wait, actually ...... how can it be seen? like how exactly would you explain that

 

[bleakarcher]

x''=-12sin(2t+5)=-4[3sin(2t+5)]=-4x
Max. acceleration occurs at endpoint ie when x=+/-3,
x''=-4*3 or -4*-3=+/-12m/s^2

 

[b3kh1t]

wait, actually ...... how can it be seen? like how exactly would you explain that

Because has the range between 1 and -1, if you sketch the sine graph. So the highest value it can take is 1, therefore the greatest acceleration is for 12X1= 12 m/s^2.

Just let me know if you still don't get it, I'll try explain it a different way =D

 

[b3kh1t]

wait, actually ...... how can it be seen? like how exactly would you explain that

Because has the range between 1 and -1, if you sketch the sine graph, as the 2t+5 in this case only dictates the period. So the highest value it can take is 1, therefore the greatest acceleration is for 12X1= 12 m/s^2.

I just look at the amplitude of the graph and say since the sine graph has the highest value of 1, then the maximum value is the amplitude.

Just let me know if you still don't get it, I'll try explain it a different way =D