Question

The displacement of a mass is given by the function y=sin3t
The tasks are to:
1. Draw a graph of the displacement y(m) against time(s) for the time t= 0s to t= 2s.
2. Identify the position of any turning points amd whether they’re maxima, minima or points of inflexion.
3. Calculate the turning points of the function using differential calculus and show which are maxima, minima or points of inflexion by using the second derivative.

Answer 1

2.$y'=3\cos3t$ hence the turning points is $t=\pi/6 s,t=\pi/2 s$ as $y'(\pi/6)=y'(\pi/2)=0$

3.$y''=-9\sin3t$ hence the inflexion point is $t=\pi/3 s$ as $y''(\pi/3)=0$ , the point of maximum is $t=\pi/6 s$ as $y''(\pi/6)<0$ , the point of minimum is $t=\pi/2 s$ as $y''(\pi/2)>0$

1.