Question

Graham, a physics enthusiast, is asked by his instructor to visit a nearby carpentry. He observed
there a hand–held powered reciprocating saw, say a sabre saw, which performs SHM in a vertical plane with
an angular frequency of 350 rad s−1
. Assume that the tip of the toothed blade of the saw is at x = 0 with
positive velocity when t = 0 and the amplitude of SHM is 2.40 cm. Write an equation, as a function of time,
which shows the position of the tip of the toothed blade. Also calculate that how much will the blade take to
travel from x = 0 to x = 1.20 cm? To 2.40 cm?

Answer 1

equation of SHM is given by:

$$x=a\sin (\omega t)$$

Here,

$$a=2.4\ cm\\ \omega=350\ red\ sec^{-1}\\So,\\x=2.4\sin(350t)$$

(a) Time from x=0 to x=1.2 cm -

$$1.2=2.4\sin(350t)\\or\\\sin(350t)=\frac{1}{2}\\or\\350t=\frac{\pi}{6}\\or\\t=0.0015\ sec$$

(b) Time from x=0 to x = 2.4 cm

$$2.4=2.4\sin(350t)\\or\\\sin(350t)=1\\or\\350t=\frac{\pi}{2}\\or\\t=0.0045\ sec$$