Question

Graham,aphysicsenthusiast,isaskedbyhisinstructortovisitanearbycarpentry. Heobserved there a hand–held powered reciprocating saw, say a sabre saw, which performs SHM in a vertical plane with an angular frequency of 350rads−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 2.40cm. 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 = 1.20cm? To 2.40cm?

Answer 1

The position of the tip of the toothed blade:

$$x(t)=A\cos{\omega t}$$

$$x(t)=0.024\cos{350 t}$$

Time from x = 0 to x = 2.40 cm:

$$\frac{T}{4}=\frac{2\pi}{4\omega}=\frac{\pi}{2(350)}=0.00449\ s=4.49\ ms$$

Time from x = 0 to x = 1.20 cm:

$$0.012=0.024\cos{350 t}$$

$$t=0.00299\ s=2.99\ ms$$