Asewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and freuency of 2.55 hz.
(a) what's the maximum speed of the needle ?
(b) what's the maximum acceleration of the needle ?

The tip of the needle to move from the highest point to the lowest point in 0.4 sec and the needle tip to travel a total distance in 0.9 sec.

Explanation:

Given that,

Frequency = 2.5 Hz

Amplitude = 1.27 cm

(a). We need to calculate the time

The frequency is the reciprocal of the time.

The time taken from highest point to lowest point

(b).  We need to calculate the time

The time taken in one cycle = 0.4 sec

The distance covered  in one sec= 4 times x amplitude

We need to calculate the speed

Using formula of speed

We need to calculate the time

Hence,  The tip of the needle to move from the highest point to the lowest point in 0.4 sec and the needle tip to travel a total distance in 0.9 sec.