1.

A needle of a sewing machine moves along a path of amplitude 4 cm with frequency 5 Hz. Find its acceleration \(\cfrac{1}{30}\)s after it has crossed the mean position.

Answer»

Data : A = 4 cm = 4 × 10-2 m, f = 5Hz, t = \(\frac{1}{30}\)s ω = 2πf = 2π (5) = 10π rad/s

Therefore, the magnitude of the acceleration,

|a| = ω2 x = ω2 A sin ωt

= (10π)2 (4 × 102)

= 10π2 sin\(\frac{\pi}{3}\) = 10 (9.872)(0.866) = 34.20 m/s2



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