SHM Question (1 Viewer)

[Kingportable]

John Fitzpatrick 3U Mathematics 25(c) Question 3


A particle movies in a straight line. At time t seconds, its displacement x cm from a fixed poin O in the line is given by x=5sin((pi/2)T + pi/6). Express the acceleration in terms of x only and hence show that the motion is simple harmonic. Find:


iii) The speed when x=-2+1/2 or x=-5/2
iv) the acceleration when x = -2 + 1/2 or x=-5/2


btw i tried using x''=-n^2 . x and v^2=n^2 . (a^2 - x^2)
My problem with differentiation from the displacement was that i didn't have a value for t

 

[23011]

x=5sin(pi/2)t +pi/6
x'= (5pi/2)cos(pi/2)t
x''= -((5pi²)/4)sin(pi/2)t
therefore equals -((pi²)/4)(5sin(pi/2)t)
which equals -(pi²)/4)(x - pi/6) since 5sin(pi/2)t = x - pi/6

you should be able to do the rest from there