In an electric shaver, the blade moves back and forth over a distance of 2.1 mm in simple harmonic motion, with frequency 116 Hz. Find (a) the amplitude, (b) the maximum blade speed, and (c) the magnitude of the maximum blade acceleration.

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DeniceSandidge DeniceSandidge · Answer 1 · 2019-09-12T07:04:03+02:00

Answer:

amplitude = 1.05×[tex]10^{-3}[/tex] m

maximum speed = 76.49 cm/s

acceleration = 557.22 m/s²

Explanation:

given data

distance = 2.1 mm

frequency = 116 Hz

to find out

amplitude , maximum speed and acceleration

solution

we will apply here amplitude formula that is

amplitude = wavelength distance / 2

so

amplitude = 2.1 /2

amplitude = 1.05 mm = 1.05×[tex]10^{-1}[/tex] cm

amplitude = 1.05×[tex]10^{-3}[/tex] m

and

maximum speed = amplitude × angular frequency

so angular frequency = 2πf

angular frequency = 2π(116)

angular frequency = 728.48 rad/s

so

maximum speed = amplitude × angular frequency

maximum speed = 1.05×[tex]10^{-1}[/tex] × 728.48

maximum speed = 76.49 cm/s

and

acceleration = amplitude × (angular frequency)²

acceleration = 1.05×[tex]10^{-3}[/tex] × (728.48)²

acceleration = 557.22 m/s²