Frequency and amplitude of a particle in simple harmonic motion a particle moves in simple harmonic motion. knowing that the maximum velocity is 200 mm/s and the maximum acceleration is 13 m/s , determine the amplitude and frequency of the motion. amplitude of the motion xm 1mm. frequency of the motion勿 hz.

amplitude, a = 3.076 mm

frequency, f = 10.35 Hz

Explanation:

Vmax = 200 mm /s = 0.2 m/s

Amax = 13 m/s

Let f be the frequency and a be the amplitude.

Use the formula of maximum velocity.

Vmax = ω a

0.2 = ω a     (1)

Use the formula of maximum acceleration.

Amax = ω^2 x a

13 = ω^2 a     (2)

Divide equation (2) by (1)

ω = 13 / 0.2 = 65 rad/s

Put in equation (1)

0.2 = 65 x a

a = 3.076 x 10^-3 m

a = 3.076 mm

Let f be the frequency

ω = 2 π f

f = 65 / (2 x 3.14) = 10.35 Hz  

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