A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 0.0127 m and a frequency of 2.55 Hz. What is the maximum speed of the needle?

v = 0.2035 m/s

Explanation:

given,

Amplitude, A = 0.0127 m

Frequency, f = 2.55 Hz

maximum speed of the needle = ?

we know,

x = A cos ω t

velocity of the motion

v = - A ω sin ω t

for maximum speed

sin ω t = 1

v = - A ω

ω = 2 π f

now,

v = A 2 π f

v = 0.0127 x 2 π x 2.55

v = 0.2035 m/s

Hence, the maximum speed of the needle is equal to 0.2035 m/s